Marichev-Saigo-Maeda Fractional Integral Operators Involving the Product of Generalized Bessel-Maitland Functions
|
|
- Alfred Horton
- 5 years ago
- Views:
Transcription
1 Bol. Soc. Para. Mat. 3s. v :????. c SPM ISSN o lie ISSN i press SPM: doi: /bspm Marichev-Saigo-Maeda Fractioal Itegral Operators Ivolvig the Product of Geeralized Bessel-Maitlad Fuctios D.L. Suthar, P. Agarwal ad Hafte Amsalu abstract: The aim of this paper is to evaluate two theorems for fractioal itegratio ivolvig Appell s fuctio F 3. due to Marichev-Saigo-Maeda, to the product of the geeralized Bessel-Maitlad fuctio. The results are expressed i terms of the multivariable geeralized Lauricella fuctios. Correspodig assertios i terms of Saigo, Erdélyi-Kober, Riema-Liouville, ad Weyl type of fractioal itegrals are also preseted. Some iterestig special cases of our two mai results are preseted. Further, we poit out also their relevace. Key Words:Geeralized Fractioal itegrals, Geeralized Bessel-Maitlad fuctio, geeralized Lauricella series i several variables, Appell fuctio-f 3.. Cotets 1 Itroductio, Defiitio ad prelimiaries 1 2 Left-Side Fractioal Itegratio of Geeralized Bessel-Maitlad Fuctios 4 3 Right-Side Fractioal Itegratio of Geeralized Bessel-Maitlad Fuctios 6 4 Cosequece Results ad Cocludig Remarks 9 1. Itroductio, Defiitio ad prelimiaries The fractioal calculus is ow a day s oe of the most fast growigsubject of mathematical aalysis. It is a field of applied mathematics that deals with derivatives ad itegrals of arbitrary orders. The fractioal itegral operator ivolvig various special fuctios has foud cosiderable importace ad applicatios i various sub-fields of applicable mathematical aalysis. May applicatios of fractioal calculus ca be foud i turbulece ad fluid dyamics, stochastic dyamical system, plasma physics ad oliear cotrol theory, image processig, oliear biological systems, astrophysics, ad i quatum mechaics. Sice last four decades, a umber of workers like Agarwal 1-3, Agarwal ad Jai 5, Baleau 8, Baleau ad Mustafa 9, Baleau et al , Kalla 14, Kalla ad Saxea 15, Kilbas 16, Kilbas ad Sebastia 17, Kiryakova 18-19, Love 20, 2010 Mathematics Subject Classificatio: 33C10. Submitted May 18, Published November 18, Typeset by B S P M style. c Soc. Para. de Mat.
2 2 D.L. Suthar, P. Agarwal ad Hafte Amsalu McBride 22, Purohit ad Kalla 25 ad Saigo 29-30, so forth have studied, i depth, the properties, applicatios, ad differet extesios of various operators of fractioal calculus. A detailed accout of geeralized fractioal calculus operators alog with their properties ad applicatios ca be foud i the research moographs by Kiryakova 18, Miller ad Ross 23, ad so forth. The computatio of fractioal derivatives ad fractioal itegrals of special fuctios of oe ad more variables is importat from the poit of view of the usefuless of these results i the evaluatio of geeralized itegrals ad the solutio of differetial ad itegral equatios. Motivated by these aveues of applicatios, a remarkably large umber of fractioal itegral formulas ivolvig a variety of special fuctios have bee developed by may authors see, e.g., 7, 26-28, 34, 35. Fractioal itegratio formulae for the Bessel fuctio ad geeralized Bessel fuctios are give recetly by Kilbas ad Sebastia 17, Malik et al. 21, Purohit et al. 28 ad Saxea et al. 32. Here, we aim at presetig compositio formula of Marichev-Saigo-Maeda fractioal itegral operators ad the product of geeralized Bessel-Maitlad fuctio, which are expressed i terms of the multivariable geeralized Lauricella fuctios. Some iterestig special cases of our mai results are also cosidered. O accout of success of the Saigo operators 29-30, i their study o various fuctio spaces ad their applicatio i the itegral equatio ad differetial equatios, Saigo ad Maeda 31 itroduced the followig geeralized fractioal itegral ad differetial operators of ay complex order with Appell fuctio F 3. i the kerel, as follows: Let α,α,β,β,γ C ad x > 0, the the geeralized fractioal calculus operators the Marichev-Saigo-Maeda operators ivolvig the Appell fuctio, or Hor s F 3 -fuctio are defied by the followig equatios: where x 0 x 0+ f x = x α Γγ x t γ 1 t α F 3 α,α,β,β ;γ;1 t x,1 x ftdt, Reγ > 0, 1.1 t f x = x α Γγ t x γ 1 t α F 3 α,α,β,β ;γ;1 x t,1 t ftdt, Reγ > 0, 1.2 x F 3 α,α,β,β ;γ,x;y = m,=0 αm α β m β x m y, max{ x, y < 1}, γ +m m!! is kow as Appell fuctio kow also as Hor fuctio.
3 Marichev-Saigo-Maeda Fractioal Itegral Operators... 3 Followig Saigo ad Maeda 31, the image formulas for a power fuctio, uder operators 1.1 ad 1.2, are give by: 0+ x ρ 1 ρ, ρ+γ α α β, ρ+β α x = Γ ρ+β, ρ+γ α α, ρ+γ α x ρ α α +γ 1, β 1.3 where Rρ > max { 0, Rα+α +β γ, Rα β } ad Rγ > 0. x ρ 1 1 ρ β, 1 ρ+α+β γ, 1 ρ γ +α+α x = Γ 1 ρ, 1 ρ+α β, 1 ρ+α+α +β γ, x ρ+γ α α 1, 1.4 where Rρ < 1+mi { R β, Reα+α γ, Rα+β γ } ad Reγ > 0. represetig the fractio of may Gamma fuc-... Here we used the symbol Γ... tios. We ivestigate compositio of itegral trasforms 1.1 ad 1.2 with the product of geeralized Bessel-Maitlad fuctios J v,q µ,γ z, which is defied by Pathak 24 as follow: J v,q µ,γ z = γ qm z m Γv +µm+1 m!, 1.5 S p,p 1,p 2,...,p q,q 1,q 2,...,q m=0 where µ,v,γ C, Rµ 0, Rv 1, Rγ 0 ad q 0, 1 N, γ qm is kow as geeralized Pochhammer symbol, is defied as γ qm = Γγ+qm Γγ. Also, we show that the compositio is expressed i terms of the multivariable geeralized Lauricella fuctios due to Srivastava ad Daoust 33 is a geeralizatio of the Wright fuctio p ψ q i several variables 13 ad defied by a p : αp 1,..., α c 1 p : : γ 1 p1 p 1 ;...;c p1 : γ p 1 ; b q : β 1 q,..., β p : = m 1,m 2,...,m =0 d 1 : δ 1 q1 q1 ;...;d q1 : z 1,...,z δ q1 ; Am 1,m 2,...,m z mj j m j!, 1.6 where p k=1 a Γ j + m kα k pk j k=1 Am 1,m 2,...,m = q k=1 b Γ j + Γ c j + m kγ k j m kβ k qk j k=1 k=1 Γ d j +, m kδ k j 1.7 Thecoefficietα k j j = 1,2,...,p,βk j j = 1,2,...,q,γ k j j = 1,2,...,p kadδ k j j = 1,2,...,q k for all k = 1,...,, are real ad positive ad a p meas the arrayof p-parameters a 1,...,a p ; with similar iterpretatios for b p, γ 1 p 1, α 1 p1 ad so forth.
4 4 D.L. Suthar, P. Agarwal ad Hafte Amsalu The paper is orgaized as follow. The compositio formula of Marichev-Saigo- Maeda fractioal itegral operators 1.1 ad 1.2 with the product of geeralized Bessel-Maitlad fuctio 1.5 is proved i terms of the multivariable geeralized Lauricella fuctios 1.6 i Sectios 2 ad 3, respectively. The correspodig results for the correspodig assertios i terms of Saigo, Erdélyi-Kober, Riema- Liouville ad Weyl type of fractioal itegrals are also preseted i Sectios 2 ad 3. Special cases givig compositios of fractioal itegrals with the product of Bessel fuctios ad cocludig remarks are cosidered i Sectio Left-Side Fractioal Itegratio of Geeralized Bessel-Maitlad Fuctios I this sectio, we establish image formulas for the product of geeralized Bessel- Maitlad fuctio ivolvig left sided of Marichev-Saigo-Meada fractioal itegral operator, i term of the multivariable geeralized Lauricella fuctios. These formulas are give by the followig theorem: Theorem 2.1. Let α,α,β,β,σ,λ,γ,ν j, q j, µ j, k j, b C ad satisfyig the iequalities, Rγ > 0, Rσ > 0, Rσ > max { 0,Rα+α +β γ,r α β } ad R ν j +1 > 0 the for x > 0, ax b < 1 oe has 0+ t σ 1 b at λ a j t ρ 1 j x = xσ+γ α α Γλ b λ 1 A, Γk j S3;1;...;1;1 0 B, C, D, E : F : G; H; a 1 x ρ 1,..., a x ρ ax,, 2.1 b where A, B, C, D, E, F, G ad H are give by the followig A = σ : ρ 1,ρ 2,...,ρ,1, 2.2 B = σ +β : ρ 1,ρ 2,...,ρ,1, 2.3 C = σ +γ α α β : ρ 1,ρ 2,...,ρ,1, 2.4 D = σ +γ α α : ρ 1,ρ 2,...,ρ,1, 2.5 E = σ +β α : ρ 1,ρ 2,...,ρ,1, 2.6 F = σ +γ α β : ρ 1,ρ 2,...,ρ,1, 2.7 G = k 1 : q 1 ;...;k : q ; λ : 1, 2.8 H = v 1 +1 : µ 1 ;...;v +1 : µ ;
5 Marichev-Saigo-Maeda Fractioal Itegral Operators... 5 Proof: For the sake of coveiece, let the left-had side of the 2.1 be deoted by F. Usig defiitio 1.5 ad biomial expasio, amely, we fid F = b at λ = b λ 0+ = 0+ m=0 λ m m! m at, b t σ 1 b at λ m j=0 at b < a j t ρ j x t m σ 1 b λ λ m at m! b m=0 k j qjm j a j t ρ m j j x, 2.11 m j!γv j +µ j m j +1 Followig the covergece coditio of Theorem 2.1, for ay k N 0, R σ +m+ ρ jm j R σ + ρ jm j > max { 0,Rα+α +β γ,r α β }, 2.12 ad chagig the order of itegratio ad summatio, we obtai F = b λ m,m 1,m 2,...,m =0 k 1 q1m 1 a 1 m1 λ m a Γv 1 +µ 1 m 1 +1 m!m 1! b... k qm a m 0+ t σ+m+ρ 1 m1+...+ρ m 1 x, 2.13 Γv +µ m +1 m! Now o applyig 1.3 with ρ replaced by σ+m+ρ 1 m ρ m, we obtai F = xσ+γ α α 1 Γλ b λ Γ Γ 1 Γk j m,m 1,m 2,...,m =0 σ +m+γ α α β + ρ jm j Γ σ +m+γ α α ρ jm j Γ m Γ σ +m+ ρ jm j Γ σ +m+β + ρ jm j σ +m α +β + ρ jm j σ +m+γ α β + ρ jm j Γk 1 +q 1 m 1 Γv 1 +µ 1 m Γk +q m Γv +µ m +1 Γλ+m
6 6 D.L. Suthar, P. Agarwal ad Hafte Amsalu a 1x ρ 1 m 1 m 1!... a x ρ m m! ax b m! m I accordace with 1.6, gives the required result 2.1. This completed the proof of the Theorem 2.1. Now, we preset some special cases of Theorem 2.1 are give below: O settig α = 0 i Theorem 2.1, we get the followig Saigo fractioal itegral image of the product of geeralized Bessel-Maitlad fuctio. Corollary 2.2. Let α,β,β,σ,λ,γ,ν j, q j, µ j, k j, b C ad x > 0, ax b < 1 satisfyig the iequalities, Rγ > 0, Rσ > 0, R ν j +1 > 0 the there holds the results: I γ,α γ, β 0+ t σ 1 b at λ a j t ρ j x = xσ+γ α 1 Γλ b λ 1 A, Γk j S2;1;...;1;1 0 D, C : F : G; H; a 1 x ρ 1,..., a x ρ ax,. b 2.15 where A, C, D, F, G ad H are give by 2.2, 2.4, 2.5, 2.7, 2.8 ad 2.9 respectively. Agai, o lettig α = 0 ad α = 0 i Theorem 2.1, we get the Riema-Liouville fractioal image of the product of geeralized Bessel-Maitlad fuctio; asserted by the followig corollary. Corollary 2.3. Let α,β,β,σ,λ,γ,ν j, q j, µ j, k j, b C ad x > 0, ax b < 1 satisfyig the iequalities, Rγ > 0, Rσ > 0, R ν j +1 > 0 the there holds the results: I γ 0+ t σ 1 b at λ a j t ρ j x = xσ+γ 1 Γλ b λ 1 Γk j S1;1;...;1; 1 A : 0 D : G; H; a 1 x ρ 1,..., a x ρ ax, b where A, D, G ad H are give by 2.2, 2.5, 2.8 ad 2.9 respectively.
7 Marichev-Saigo-Maeda Fractioal Itegral Operators Right-Side Fractioal Itegratio of Geeralized Bessel-Maitlad Fuctios I this sectio, we establish image formulas for the product of geeralized Bessel- Maitlad fuctio ivolvig right sided of Marichev-Saigo-Meada fractioal itegral operator, i term of the multivariable geeralized Lauricella fuctios. These formulas are give by the followig theorem: Theorem 3.1. Let α,α,β,β,σ,λ, γ, ν j, q j, µ j, k j, b C ad satisfyig the iequalities, Rγ > 0, Rσ < 1 + mi { R β,rα+α γ,r α+β γ } Rσ > 0, ad R ν j +1 > 0 the for x > 0, a < 1 oe has t σ 1 b a/t λ bx a j /t ρ 1 j x = xσ+γ α α Γλ b λ 1 A0, Γk j S3;1;...;1;1 3;1;...;1;0 B 0, C 0, D 0, E 0 : F 0 : G 0 ; H 0 ; a 1 x ρ 1,..., a x ρ, a, 3.1 bx where A 0, B 0, C 0, D 0, E 0 ad F 0 are give by the followig: A 0 = 1 σ β : ρ 1,ρ 2,...,ρ, 1, 3.2 B 0 = 1 σ : ρ 1,ρ 2,...,ρ, 1, 3.3 C 0 = 1 σ γ +α+α : ρ 1,ρ 2,...,ρ, 1, 3.4 D 0 = 1 σ +α β : ρ 1,ρ 2,...,ρ, 1, 3.5 E 0 = 1 σ +α+β γ : ρ 1,ρ 2,...,ρ, 1, 3.6 F 0 = 1 σ +α+α +β γ : ρ 1,ρ 2,...,ρ, 1, 3.7 ad G, H are give by 2.8 ad 2.9, respectively. Proof: For coveiece, Let the left-had side of the 3.1 be deoted by F. Usig defiitio 1.5 ad biomial expasio, we fid F = t σ 1 b a/t λ a j /t ρ j x = t σ 1 b λ λ m a m m! bt m=0 k j qjm j a j /t ρ j m j x, 3.8 m j!γv j +µ j m j +1 m j=0
8 8 D.L. Suthar, P. Agarwal ad Hafte Amsalu Followig the covergece coditio of Theorem 3.1, for ay k N 0, R σ m ρ j m j R σ ρ j m j < 1+mi { R β,rα+α γ,r α+β γ }, 3.9 ad chagig the order of itegratio ad summatio, we obtai F = b λ m,m 1,m 2,...,m =0 k 1 q1m 1 a 1 m1 λ m a Γv 1 +µ 1 m 1 +1 m!m 1! b... k qm a m t σ m ρ 1 m1... ρ m 1 x, 3.10 Γv +µ m +1 m! Now o applyig 1.3 with ρ replaced by σ+m+ρ 1 m ρ m, we obtai F = xσ+γ α α 1 Γλ b λ 1 Γk j m,m 1,m 2,...,m =0 m Γ 1 σ β +m+ ρ jm j Γ 1 σ +m+ ρ j m j Γ 1 σ+α+β γ +m+ ρ jm j Γ 1 σ +α+α +β γ +m+ ρ j m j Γ 1 σ γ +α+α +m+ ρ jm j Γ 1 σ +α β +m+ ρ j m j Γk 1 +q 1 m 1 Γv 1 +µ 1 m Γk +q m Γv +µ m +1 Γλ+m a 1/x ρ 1 m 1 m 1!... a /x ρ m m! a m bx m! I accordace with 1.6, gives the required result 3.1. This completed the proof of the Theorem 3.1. Now, we preset some special cases of Theorem 3.1 are give below: O settig α = 0 i Theorem 3.1, we get the followig Saigo fractioal itegral image of the product of geeralized Bessel-Maitlad fuctio.
9 Marichev-Saigo-Maeda Fractioal Itegral Operators... 9 Corollary 3.2. Let α,β,β,σ,λ,γ,ν j, q j, µ j, k j, b C ad x > 0, a bx < 1 satisfyig the iequalities, Rγ > 0, Rσ > 0, R ν j +1 > 0 the there holds the results: = xσ+γ α 1 Γλ b λ I γ,α γ, β t σ 1 b a/t λ 1 A0, Γk j S2;1;...;1;1 2;1;...;1;0 B 0, C 0 : D 0 : a j /t ρ j x G; H; a 1 x ρ 1,..., a x ρ, a bx where A 0, B 0, C 0 ad D 0 are give by 3.2, 3.3, 3.4 ad 3.5 respectively. Agai, o lettig α = 0 ad α = 0 i Theorem 3.1, we get the Riema-Liouville fractioal image of the product of geeralized Bessel-Maitlad fuctio; asserted by the followig corollary. Corollary 3.3. Let α,β,β,σ,λ,γ,ν j, q j, µ j, k j, b C ad x > 0, a bx < 1 satisfyig the iequalities, Rγ > 0, Rσ > 0, R ν j +1 > 0 the there holds the results: = xσ+γ 1 Γλ b λ I γ t σ 1 b a/t λ 1 C0 : Γk j S1;1;...;1;1 1;1;...;1;0 B 0 : a j /t ρ j x G; H; a 1 x ρ 1,..., a x ρ, a bx where B 0, C 0, G ad H are give by 3.3, 3.4, 2.8 ad 2.9 respectively. 4. Cosequece Results ad Cocludig Remarks I this sectio, we briefly cosider aother variatio of the results derived i the precedig sectios. Bessel-Maitlad fuctios are importat special fuctios that appear widely i sciece ad egieerig. Bessel-Maitlad fuctios are oscillatory ad may be regarded as geeralizatios of Bessel fuctios. Further, it ca be easily see that for q = 1, γ = 1 ad v is replaced by v +σ ad z is replaced by z 2 /4, the geeralized Bessel-Maitlad fuctio 1.5 reduces to J v,σ µ z which is defied by Agarwal et al. 6, ad whe q = 0 the fuctio reduces to geeralized Bessel fuctio J v µ z defied by Agarwal 4. Similarly whe q = 0, µ = 1 ad z is replaced by z 2 /4, the geeralizedbessel-maitlad fuctio 1.5 reduces to Bessel s fuctio J v z of the first kid of order v, ad whe q = 0 ad v is replaced by v 1 ad z is replaced by z reduces to Wright fuctio φµ,v;z which is defied by defied by Choi et al. 12. Therefore, the results preseted i this paper are easily coverted i terms of the various special Bessel fuctios after some suitable parametric replacemet.
10 10 D.L. Suthar, P. Agarwal ad Hafte Amsalu The geeralized Bessel-Maitlad fuctio defied by 1.5, possess the advatage that a umber of Bessel fuctios, Mittag-Leffler fuctio, trigoometric fuctios ad hyperbolic fuctios happe to be the particular cases of this fuctio. Therefore, we coclude this paper with the remark that, the results deduced above are sigificat ad ca lead to yield umerous other fractioal itegrals ivolvig various Bessel fuctios ad trigoometric fuctios by the suitable specializatios of arbitrary parameters i the theorems. More importatly, they are expected to fid some applicatios to the solutios of fractioal differetial ad itegral equatios. The results thus derived i this paper are geeral i character ad likely to fid certai applicatios i the theory of special fuctios. Refereces 1. Agarwal, P., Further results o fractioal calculus of Saigo operators, Appl. Appl. Math., 7, 2, , Agarwal, P., Geeralized fractioal itegratio of the H fuctio, Matematiche Cataia, 67, 2, , Agarwal, P., Fractioal itegratio of the product of two multivariables H-fuctio ad a geeral class of polyomials, Advaces i Applied Mathematics ad Approximatio Theory, Spriger Proc. Math. Stat., Spriger, New York, 41, , Agarwal, P., Pathway fractioal itegral formulas ivolvig Bessel fuctio of the first kid, Adv. Stud. Cotemp. Math., 25, 1, , Agarwal, P., Jai, S., Further results o fractioal calculus of Srivastava polyomials, Bull. Math. Aal. Appl., 3, 2, , Agarwal, P., Jai, S., Chad, M., Dwivedi, S.K., Kumar, S., Bessel fuctios associated with Saigo-Maeda fractioal derivatives operators, J. Fract. Calc. Appl., 5, 2, , Agarwal, P., Purohit, S.D., The uified pathway fractioal itegral formulae, J. Fract. Calc. Appl., 4, 1, , Baleau, D., About fractioal quatizatio ad fractioal variatioal priciples, Commu Noliear Sci Numer Simul., 14, 6, , Baleau, D., Mustafa, O.G., O the global existece of solutios to a class of fractioal differetial equatios, Comput. Math. Appl., 59, 5, , Baleau, D., Mustafa, O.G., Agarwal, R.P., O the solutio set for a class of sequetial fractioal differetial equatios, J. Phys. A, 43, 38, Article ID , Baleau, D., Mustafa, O.G., O Rega, D., A uiqueess criterio for fractioal differetial equatios with Caputo derivative, Noliear Dyam., 71, 4, , Choi, J., Agarwal, P., Mathur, S., Purohit, S.D., Certai ew itegral formulas ivolvig the geeralized Bessel fuctios, Bull. Korea Math. Soc., 51, 4, , Exto, H., Multiple Hypergeometric Fuctios ad Applicatios, Foreword by L. J. Slater. Mathematics & its Applicatios. Ellis Horwood Ltd., Chichester; Halsted Press Joh Wiley & Sos, Ic., New York-Lodo-Sydey, 312, Kalla, S.L., Itegral operators ivolvig Fox s H-fuctio, Acta Mexicaa Ci. Tec., 3, , Kalla, S.L., Saxea, R.K., Itegral operators ivolvig hypergeometric fuctios, Math. Z., 108, , Kilbas, A.A., Fractioal calculus of the geeralized Wright fuctio, Fract. Calc. Appl. Aal., 8, 2, , 2005.
11 Marichev-Saigo-Maeda Fractioal Itegral Operators Kilbas, A.A., Sebastia, N., Geeralized fractioal itegratio of Bessel fuctio of the first kid, Itegral Trasforms Spec. Fuct., 19, 11-12, , Kiryakova,V., Geeralized Fractioal Calculus ad Applicatios, Pitma Research Notes i Mathematics Series, 301. Logma Scietific & Techical, Harlow; copublished i the Uited States with Joh Wiley & Sos, Ic., New York, Kiryakova,V., A brief story about the operators of the geeralized fractioal calculus, Fract. Calc. Appl. Aal., 11, 2, , Love, E.R., Some itegral equatios ivolvig hypergeometric fuctios, Proc. Ediburgh Math. Soc., 15, 3, , Malik, P., Modal, S.R., Swamiatha, A., Fractioal Itegratio of Geeralized Bessel Fuctio of the First Kid, IDETC/CIE, McBride, A.C., Fractioal powers of a class of ordiary differetial operators, Proc. Lodo Math. Soc., 45, 3, , Miller, K.S., Ross, B., A Itroductio to the Fractioal Calculus ad Fractioal Differetial Equatios, A Wiley-Itersciece Publicatio. Joh Wiley & Sos, Ic., New York, Pathak, R.S., Certai covergece theorems ad asymptotic properties of a geeralizatio of Lommel ad Maitlad trasformatios, Proc. Nat. Acad. Sci. Idia Sect. A, 36, 1, 81-86, Purohit, S.D., Kalla, S.L., O fractioal partial differetial equatios related to quatum mechaics, J. Phys. A, 44, 4, Article ID , Purohit, S.D., Suthar, D.L., Kalla, S.L., Some results o fractioal calculus operators associated with the M-fuctio, Hadroic J., 33, 3, , Purohit, S.D., Kalla, S.L., Suthar, D.L., Fractioal itegral operators ad the multiidex Mittag-Leffler fuctios, Sci. Ser. A Math. Sci. N.S., 21, 87-96, Purohit, S.D., Suthar, D.L., Kalla, S.L., Marichev-Saigo- Maeda fractioal itegratio operators of the Bessel fuctio, Matematiche Cataia, 67, 1, 21-32, Saigo, M., A remark o itegral operators ivolvig the Gauss hypergeometric fuctios, Math. Rep. Kyushu Uiv., 11, 2, , Saigo, M., A certai boudary value problem for the Euler- Darboux equatio, Math. Japo., 24, 4, , Saigo, M., Maeda, N., More geeralizatio of fractioal calculus, Trasform methods & special fuctios, Vara 96, Bulgaria Acad. Sci., Sofia, , Saxea, R.K., Ram, J., Kumar, D., Geeralized fractioal itegratio of the product of Bessel fuctios of the first kid, Proceedigs of the 9th Aual Coferece of the Society for Special Fuctios ad their Applicatios SSFA. Soc. Spec. Fuct. Appl., Cheai, 9, 15-27, Srivastava, H.M., Daoust, M.C., Certai geeralized Neuma expasios associated with the Kampé de Fériet fuctio, Nederl. Akad. Wetesch. Proc. Ser. A 72 = Idag. Math., 31, , Suthar, D.L., Amsalu, H., Certai itegrals associated with the geeralized Bessel-Maitlad fuctio, Appl. Appl. Math., 12, 2, , Suthar, D.L., Habeom, H., Itegrals ivolvig geeralized Bessel-Maitlad Fuctio, J. Sci. Arts, 37, 4,
12 12 D.L. Suthar, P. Agarwal ad Hafte Amsalu D.L. Suthar, Departmet of Mathematics, Wollo Uiversity, P.O.Box: 1145, Dessie, South Wollo, Amhara Regio, ETHIOPIA. address: ad P. Agarwal, Departmet of Mathematics, Aad Iteratioal College of Egieerig, Jaipur, , Rajastha, INDIA. address: ad Hafte Amsalu, Departmet of Mathematics, Wollo Uiversity, P.O. Box: 1145, Dessie, South Wollo, Amhara Regio, ETHIOPIA. address:
Research Article Certain Fractional Integral Formulas Involving the Product of Generalized Bessel Functions
Hidawi Publishig Corporatio The Scietific World Joural Volume 2013, Article ID 567132, 9 pages http://dx.doi.org/10.1155/2013/567132 Research Article Certai Fractioal Itegral Formulas Ivolvig the Product
More informationarxiv: v1 [math.ca] 22 Jan 2019
ON A NEW TYPE MULTIVARIABLE HYPERGEOMETRIC FUNCTIONS D. KORKMAZ-DUZGUN AND E. ERKUŞ-DUMAN arxiv:1901.07551v1 [math.ca] 22 Ja 2019 Abstract. I this paper, we defie a ew type multivariable hypergeometric
More informationIntegral Formulas Involving Product of General Class of Polynomials and Generalized Bessel Function
Sohag J. Math. 3, No., 77-81 77 Sohag Joural of Mathematics A Iteratioal Joural http://.doi.org/1.18576/sjm/35 Itegral Formulas Ivolvig Product of Geeral Class of Polomials ad Geeralized Bessel Fuctio
More information( ) ( ) Page 339 Research Guru: Online Journal of Multidisciplinary Subjects (Peer Reviewed)
Marichev-Saigo Maeda Fractional Calculus Operators and the Image Formulas of the Product of Generalized Gauss Hypergeometric Function and the K-Function Javid Majid, Aarif Hussain, Imtiyaz, Shakir Hussain
More informationOn Bilateral Generating Relation for a Sequence of Functions
It. Joural of Math. Aalysis, Vol. 2, 2008, o. 8, 383-389 O Bilateral Geeratig Relatio for a Sequece of Fuctios A. K. Shukla ad J. C. Prajapati Departmet of Mathematics S.V. Natioal Istitute of Techology,
More informationCommon Coupled Fixed Point of Mappings Satisfying Rational Inequalities in Ordered Complex Valued Generalized Metric Spaces
IOSR Joural of Mathematics (IOSR-JM) e-issn: 78-578, p-issn:319-765x Volume 10, Issue 3 Ver II (May-Ju 014), PP 69-77 Commo Coupled Fixed Poit of Mappigs Satisfyig Ratioal Iequalities i Ordered Complex
More informationHarmonic Number Identities Via Euler s Transform
1 2 3 47 6 23 11 Joural of Iteger Sequeces, Vol. 12 2009), Article 09.6.1 Harmoic Number Idetities Via Euler s Trasform Khristo N. Boyadzhiev Departmet of Mathematics Ohio Norther Uiversity Ada, Ohio 45810
More informationMAJORIZATION PROBLEMS FOR SUBCLASSES OF ANALYTIC FUNCTIONS INVOLVING
Iteratioal Joural of Civil Egieerig ad Techology (IJCIET) Volume 9, Issue, November 08, pp. 97 0, Article ID: IJCIET_09 6 Available olie at http://www.ia aeme.com/ijciet/issues.asp?jtypeijciet&vtype 9&IType
More informationInteresting Series Associated with Central Binomial Coefficients, Catalan Numbers and Harmonic Numbers
3 47 6 3 Joural of Iteger Sequeces Vol. 9 06 Article 6.. Iterestig Series Associated with Cetral Biomial Coefficiets Catala Numbers ad Harmoic Numbers Hogwei Che Departmet of Mathematics Christopher Newport
More informationSome families of generating functions for the multiple orthogonal polynomials associated with modified Bessel K-functions
J. Math. Aal. Appl. 297 2004 186 193 www.elsevier.com/locate/jmaa Some families of geeratig fuctios for the multiple orthogoal polyomials associated with modified Bessel K-fuctios M.A. Özarsla, A. Altı
More informationEXPANSION FORMULAS FOR APOSTOL TYPE Q-APPELL POLYNOMIALS, AND THEIR SPECIAL CASES
LE MATEMATICHE Vol. LXXIII 208 Fasc. I, pp. 3 24 doi: 0.448/208.73.. EXPANSION FORMULAS FOR APOSTOL TYPE Q-APPELL POLYNOMIALS, AND THEIR SPECIAL CASES THOMAS ERNST We preset idetities of various kids for
More informationNEW FAST CONVERGENT SEQUENCES OF EULER-MASCHERONI TYPE
UPB Sci Bull, Series A, Vol 79, Iss, 207 ISSN 22-7027 NEW FAST CONVERGENT SEQUENCES OF EULER-MASCHERONI TYPE Gabriel Bercu We itroduce two ew sequeces of Euler-Mascheroi type which have fast covergece
More informationBangi 43600, Selangor Darul Ehsan, Malaysia (Received 12 February 2010, accepted 21 April 2010)
O Cesáro Meas of Order μ for Outer Fuctios ISSN 1749-3889 (prit), 1749-3897 (olie) Iteratioal Joural of Noliear Sciece Vol9(2010) No4,pp455-460 Maslia Darus 1, Rabha W Ibrahim 2 1,2 School of Mathematical
More informationON GENERALIZATION OF SISTER CELINE S POLYNOMIALS
Palestie Joural of Mathematics Vol. 5() (6), 5 Palestie Polytechic Uiversity-PPU 6 ON GENERALIZATION OF SISTER CELINE S POLYNOMIALS Khursheed Ahmad, M. Kamarujjama ad M. Ghayasuddi Commuicated by Jose
More informationSOME RELATIONS ON HERMITE MATRIX POLYNOMIALS. Levent Kargin and Veli Kurt
Mathematical ad Computatioal Applicatios, Vol. 18, No. 3, pp. 33-39, 013 SOME RELATIONS ON HERMITE MATRIX POLYNOMIALS Levet Kargi ad Veli Kurt Departmet of Mathematics, Faculty Sciece, Uiversity of Adeiz
More informationNumerical integration of analytic functions
Numerical itegratio of aalytic fuctios Gradimir V. Milovaović, Dobrilo Ð Tošić, ad Miloljub Albijaić Citatio: AIP Cof. Proc. 1479, 146 212); doi: 1.163/1.4756325 View olie: http://dx.doi.org/1.163/1.4756325
More informationGEOMETRIC PROPERTIES OF FRACTIONAL DIFFUSION EQUATION OF THE PROBABILITY DENSITY FUNCTION IN A COMPLEX DOMAIN
Pak. J. Statist. 2015 Vol. 31(5), 601-608 GEOMETRIC PROPERTIES OF FRACTIONAL DIFFUSION EQUATION OF THE PROBABILITY DENSITY FUNCTION IN A COMPLEX DOMAIN Rabha W. Ibrahim 1, Hiba F. Al-Jaaby 2 ad M.Z. Ahmad
More informationSolution of Differential Equation from the Transform Technique
Iteratioal Joural of Computatioal Sciece ad Mathematics ISSN 0974-3189 Volume 3, Number 1 (2011), pp 121-125 Iteratioal Research Publicatio House http://wwwirphousecom Solutio of Differetial Equatio from
More informationOn the Variations of Some Well Known Fixed Point Theorem in Metric Spaces
Turkish Joural of Aalysis ad Number Theory, 205, Vol 3, No 2, 70-74 Available olie at http://pubssciepubcom/tjat/3/2/7 Sciece ad Educatio Publishig DOI:0269/tjat-3-2-7 O the Variatios of Some Well Kow
More informationA note on the p-adic gamma function and q-changhee polynomials
Available olie at wwwisr-publicatioscom/jmcs J Math Computer Sci, 18 (2018, 11 17 Research Article Joural Homepage: wwwtjmcscom - wwwisr-publicatioscom/jmcs A ote o the p-adic gamma fuctio ad q-chaghee
More informationWeighted Approximation by Videnskii and Lupas Operators
Weighted Approximatio by Videsii ad Lupas Operators Aif Barbaros Dime İstabul Uiversity Departmet of Egieerig Sciece April 5, 013 Aif Barbaros Dime İstabul Uiversity Departmet Weightedof Approximatio Egieerig
More informationSufficient Conditions for Subordination of Meromorphic Functions
Joural of Mathematics ad Statistics 5 (3):4-45 2009 ISSN 549-3644 2009 Sciece Publicatios Sufficiet Coditios for Subordiatio of Meromorphic Fuctios Rabha W. Ibrahim ad Maslia arus School of Mathematical
More informationON POINTWISE BINOMIAL APPROXIMATION
Iteratioal Joural of Pure ad Applied Mathematics Volume 71 No. 1 2011, 57-66 ON POINTWISE BINOMIAL APPROXIMATION BY w-functions K. Teerapabolar 1, P. Wogkasem 2 Departmet of Mathematics Faculty of Sciece
More informationA collocation method for singular integral equations with cosecant kernel via Semi-trigonometric interpolation
Iteratioal Joural of Mathematics Research. ISSN 0976-5840 Volume 9 Number 1 (017) pp. 45-51 Iteratioal Research Publicatio House http://www.irphouse.com A collocatio method for sigular itegral equatios
More informationOn Summability Factors for N, p n k
Advaces i Dyamical Systems ad Applicatios. ISSN 0973-532 Volume Number 2006, pp. 79 89 c Research Idia Publicatios http://www.ripublicatio.com/adsa.htm O Summability Factors for N, p B.E. Rhoades Departmet
More informationOscillation and Property B for Third Order Difference Equations with Advanced Arguments
Iter atioal Joural of Pure ad Applied Mathematics Volume 3 No. 0 207, 352 360 ISSN: 3-8080 (prited versio); ISSN: 34-3395 (o-lie versio) url: http://www.ijpam.eu ijpam.eu Oscillatio ad Property B for Third
More information(p, q)-type BETA FUNCTIONS OF SECOND KIND
Adv. Oper. Theory 6, o., 34 46 http://doi.org/.34/aot.69. ISSN: 538-5X electroic http://aot-math.org p, q-type BETA FUNCTIONS OF SECOND KIND ALI ARAL ad VIJAY GUPTA Commuicated by A. Kamisa Abstract. I
More informationGenerating Functions for Laguerre Type Polynomials. Group Theoretic method
It. Joural of Math. Aalysis, Vol. 4, 2010, o. 48, 257-266 Geeratig Fuctios for Laguerre Type Polyomials α of Two Variables L ( xy, ) by Usig Group Theoretic method Ajay K. Shula* ad Sriata K. Meher** *Departmet
More informationPoincaré Problem for Nonlinear Elliptic Equations of Second Order in Unbounded Domains
Advaces i Pure Mathematics 23 3 72-77 http://dxdoiorg/4236/apm233a24 Published Olie Jauary 23 (http://wwwscirporg/oural/apm) Poicaré Problem for Noliear Elliptic Equatios of Secod Order i Ubouded Domais
More informationAsymptotic distribution of products of sums of independent random variables
Proc. Idia Acad. Sci. Math. Sci. Vol. 3, No., May 03, pp. 83 9. c Idia Academy of Scieces Asymptotic distributio of products of sums of idepedet radom variables YANLING WANG, SUXIA YAO ad HONGXIA DU ollege
More informationComparison Study of Series Approximation. and Convergence between Chebyshev. and Legendre Series
Applied Mathematical Scieces, Vol. 7, 03, o. 6, 3-337 HIKARI Ltd, www.m-hikari.com http://d.doi.org/0.988/ams.03.3430 Compariso Study of Series Approimatio ad Covergece betwee Chebyshev ad Legedre Series
More informationNumerical solution of Bagley-Torvik equation using Chebyshev wavelet operational matrix of fractional derivative
It. J. Adv. Appl. Math. ad Mech. () (04) 83-9 ISSN: 347-59 Available olie at www.iaamm.com Iteratioal Joural of Advaces i Applied Mathematics ad Mechaics Numerical solutio of Bagley-Torvik equatio usig
More informationTaylor polynomial solution of difference equation with constant coefficients via time scales calculus
TMSCI 3, o 3, 129-135 (2015) 129 ew Treds i Mathematical Scieces http://wwwtmscicom Taylor polyomial solutio of differece equatio with costat coefficiets via time scales calculus Veysel Fuat Hatipoglu
More informationSHARP INEQUALITIES INVOLVING THE CONSTANT e AND THE SEQUENCE (1 + 1/n) n
SHARP INEQUALITIES INVOLVING THE CONSTANT e AND THE SEQUENCE + / NECDET BATIR Abstract. Several ew ad sharp iequalities ivolvig the costat e ad the sequece + / are proved.. INTRODUCTION The costat e or
More informationCharacterizations Of (p, α)-convex Sequences
Applied Mathematics E-Notes, 172017, 77-84 c ISSN 1607-2510 Available free at mirror sites of http://www.math.thu.edu.tw/ ame/ Characterizatios Of p, α-covex Sequeces Xhevat Zahir Krasiqi Received 2 July
More informationPAijpam.eu ON TENSOR PRODUCT DECOMPOSITION
Iteratioal Joural of Pure ad Applied Mathematics Volume 103 No 3 2015, 537-545 ISSN: 1311-8080 (prited versio); ISSN: 1314-3395 (o-lie versio) url: http://wwwijpameu doi: http://dxdoiorg/1012732/ijpamv103i314
More informationUPPER ESTIMATE FOR GENERAL COMPLEX BASKAKOV SZÁSZ OPERATOR. 1. Introduction
Joural of Classical Aalysis Volume 7, Number 1 2015, 17 23 doi:10.7153/jca-07-02 UPPER ESTIMATE FOR GENERAL COMPLEX BASKAKOV SZÁSZ OPERATOR VIJAY GUPTA AND GANCHO TACHEV Abstract. I the preset article,
More information1 6 = 1 6 = + Factorials and Euler s Gamma function
Royal Holloway Uiversity of Lodo Departmet of Physics Factorials ad Euler s Gamma fuctio Itroductio The is a self-cotaied part of the course dealig, essetially, with the factorial fuctio ad its geeralizatio
More informationQuadratic Transformations of Hypergeometric Function and Series with Harmonic Numbers
Quadratic Trasformatios of Hypergeometric Fuctio ad Series with Harmoic Numbers Marti Nicholso I this brief ote, we show how to apply Kummer s ad other quadratic trasformatio formulas for Gauss ad geeralized
More informationInternational Journal of Mathematical Archive-3(4), 2012, Page: Available online through ISSN
Iteratioal Joural of Mathematical Archive-3(4,, Page: 544-553 Available olie through www.ima.ifo ISSN 9 546 INEQUALITIES CONCERNING THE B-OPERATORS N. A. Rather, S. H. Ahager ad M. A. Shah* P. G. Departmet
More informationUniform Strict Practical Stability Criteria for Impulsive Functional Differential Equations
Global Joural of Sciece Frotier Research Mathematics ad Decisio Scieces Volume 3 Issue Versio 0 Year 03 Type : Double Blid Peer Reviewed Iteratioal Research Joural Publisher: Global Jourals Ic (USA Olie
More informationStability of fractional positive nonlinear systems
Archives of Cotrol Scieces Volume 5(LXI), 15 No. 4, pages 491 496 Stability of fractioal positive oliear systems TADEUSZ KACZOREK The coditios for positivity ad stability of a class of fractioal oliear
More informationTRACES OF HADAMARD AND KRONECKER PRODUCTS OF MATRICES. 1. Introduction
Math Appl 6 2017, 143 150 DOI: 1013164/ma201709 TRACES OF HADAMARD AND KRONECKER PRODUCTS OF MATRICES PANKAJ KUMAR DAS ad LALIT K VASHISHT Abstract We preset some iequality/equality for traces of Hadamard
More informationDiscrete Orthogonal Moment Features Using Chebyshev Polynomials
Discrete Orthogoal Momet Features Usig Chebyshev Polyomials R. Mukuda, 1 S.H.Og ad P.A. Lee 3 1 Faculty of Iformatio Sciece ad Techology, Multimedia Uiversity 75450 Malacca, Malaysia. Istitute of Mathematical
More informationON TWO EXACT SOLUTIONS OF TIME FRACTIONAL HEAT EQUATIONS USING DIFFERENT TRANSFORMS
Ibrahim, R. W., et al.: O Two Exact Solutios of Time Fractioal Heat Equatios THERMA SCIENCE, Year 05, Vol. 9, Suppl., pp. S43-S49 S43 ON TWO EXACT SOUTIONS OF TIME FRACTIONA HEAT EQUATIONS USING DIFFERENT
More informationApplications of geometric function theory related to mechanical systems
Rev Téc Ig Uiv Zulia Vol 9 Nº 77-84 06 Applicatios of geometric fuctio theory related to mechaical systems CRamachadra ad RAmbrosePrabhu Departmet of Mathematics Uiversity College of Egieerig Villupuram
More informationThe Sumudu transform and its application to fractional differential equations
ISSN : 30-97 (Olie) Iteratioal e-joural for Educatio ad Mathematics www.iejem.org vol. 0, No. 05, (Oct. 03), 9-40 The Sumudu trasform ad its alicatio to fractioal differetial equatios I.A. Salehbhai, M.G.
More informationGENERALIZED HARMONIC NUMBER IDENTITIES AND A RELATED MATRIX REPRESENTATION
J Korea Math Soc 44 (2007), No 2, pp 487 498 GENERALIZED HARMONIC NUMBER IDENTITIES AND A RELATED MATRIX REPRESENTATION Gi-Sag Cheo ad Moawwad E A El-Miawy Reprited from the Joural of the Korea Mathematical
More informationDecoupling Zeros of Positive Discrete-Time Linear Systems*
Circuits ad Systems,,, 4-48 doi:.436/cs..7 Published Olie October (http://www.scirp.org/oural/cs) Decouplig Zeros of Positive Discrete-Time Liear Systems* bstract Tadeusz Kaczorek Faculty of Electrical
More informationA NEW CLASS OF 2-STEP RATIONAL MULTISTEP METHODS
Jural Karya Asli Loreka Ahli Matematik Vol. No. (010) page 6-9. Jural Karya Asli Loreka Ahli Matematik A NEW CLASS OF -STEP RATIONAL MULTISTEP METHODS 1 Nazeeruddi Yaacob Teh Yua Yig Norma Alias 1 Departmet
More informationSeries with Central Binomial Coefficients, Catalan Numbers, and Harmonic Numbers
3 47 6 3 Joural of Iteger Sequeces, Vol. 5 (0), Article..7 Series with Cetral Biomial Coefficiets, Catala Numbers, ad Harmoic Numbers Khristo N. Boyadzhiev Departmet of Mathematics ad Statistics Ohio Norther
More information1. Introduction. g(x) = a 2 + a k cos kx (1.1) g(x) = lim. S n (x).
Georgia Mathematical Joural Volume 11 (2004, Number 1, 99 104 INTEGRABILITY AND L 1 -CONVERGENCE OF MODIFIED SINE SUMS KULWINDER KAUR, S. S. BHATIA, AND BABU RAM Abstract. New modified sie sums are itroduced
More informationMatrix representations of Fibonacci-like sequences
NTMSCI 6, No. 4, 03-0 08 03 New Treds i Mathematical Scieces http://dx.doi.org/0.085/tmsci.09.33 Matrix represetatios of Fiboacci-like sequeces Yasemi Tasyurdu Departmet of Mathematics, Faculty of Sciece
More informationA solid Foundation for q-appell Polynomials
Advaces i Dyamical Systems ad Applicatios ISSN 0973-5321, Volume 10, Number 1, pp. 27 35 2015) http://campus.mst.edu/adsa A solid Foudatio for -Appell Polyomials Thomas Erst Uppsala Uiversity Departmet
More informationSome Approximate Fixed Point Theorems
It. Joural of Math. Aalysis, Vol. 3, 009, o. 5, 03-0 Some Approximate Fixed Poit Theorems Bhagwati Prasad, Bai Sigh ad Ritu Sahi Departmet of Mathematics Jaypee Istitute of Iformatio Techology Uiversity
More informationOn the convergence rates of Gladyshev s Hurst index estimator
Noliear Aalysis: Modellig ad Cotrol, 2010, Vol 15, No 4, 445 450 O the covergece rates of Gladyshev s Hurst idex estimator K Kubilius 1, D Melichov 2 1 Istitute of Mathematics ad Iformatics, Vilius Uiversity
More informationII. EXPANSION MAPPINGS WITH FIXED POINTS
Geeralizatio Of Selfmaps Ad Cotractio Mappig Priciple I D-Metric Space. U.P. DOLHARE Asso. Prof. ad Head,Departmet of Mathematics,D.S.M. College Jitur -431509,Dist. Parbhai (M.S.) Idia ABSTRACT Large umber
More informationNew Inequalities For Convex Sequences With Applications
It. J. Ope Problems Comput. Math., Vol. 5, No. 3, September, 0 ISSN 074-87; Copyright c ICSRS Publicatio, 0 www.i-csrs.org New Iequalities For Covex Sequeces With Applicatios Zielaâbidie Latreuch ad Beharrat
More informationModified Decomposition Method by Adomian and. Rach for Solving Nonlinear Volterra Integro- Differential Equations
Noliear Aalysis ad Differetial Equatios, Vol. 5, 27, o. 4, 57-7 HIKARI Ltd, www.m-hikari.com https://doi.org/.2988/ade.27.62 Modified Decompositio Method by Adomia ad Rach for Solvig Noliear Volterra Itegro-
More informationGeneralized Gronwall fractional summation inequalities and their applications
Xu ad Zhag Joural of Iequalities ad Applicatios (2015) 2015:242 DOI 101186/s13660-015-0763-8 R E S E A R C H Ope Access Geeralized Growall fractioal summatio iequalities ad their applicatios Ru Xu 1* ad
More informationAdvanced Analysis. Min Yan Department of Mathematics Hong Kong University of Science and Technology
Advaced Aalysis Mi Ya Departmet of Mathematics Hog Kog Uiversity of Sciece ad Techology September 3, 009 Cotets Limit ad Cotiuity 7 Limit of Sequece 8 Defiitio 8 Property 3 3 Ifiity ad Ifiitesimal 8 4
More informationThe Gamma function Michael Taylor. Abstract. This material is excerpted from 18 and Appendix J of [T].
The Gamma fuctio Michael Taylor Abstract. This material is excerpted from 8 ad Appedix J of [T]. The Gamma fuctio has bee previewed i 5.7 5.8, arisig i the computatio of a atural Laplace trasform: 8. ft
More informationSome New Iterative Methods for Solving Nonlinear Equations
World Applied Scieces Joural 0 (6): 870-874, 01 ISSN 1818-495 IDOSI Publicatios, 01 DOI: 10.589/idosi.wasj.01.0.06.830 Some New Iterative Methods for Solvig Noliear Equatios Muhammad Aslam Noor, Khalida
More informationON BLEIMANN, BUTZER AND HAHN TYPE GENERALIZATION OF BALÁZS OPERATORS
STUDIA UNIV. BABEŞ BOLYAI, MATHEMATICA, Volume XLVII, Number 4, December 2002 ON BLEIMANN, BUTZER AND HAHN TYPE GENERALIZATION OF BALÁZS OPERATORS OGÜN DOĞRU Dedicated to Professor D.D. Stacu o his 75
More informationDominant of Functions Satisfying a Differential Subordination and Applications
Domiat of Fuctios Satisfyig a Differetial Subordiatio ad Applicatios R Chadrashekar a, Rosiha M Ali b ad K G Subramaia c a Departmet of Techology Maagemet, Faculty of Techology Maagemet ad Busiess, Uiversiti
More informationSOME TRIGONOMETRIC IDENTITIES RELATED TO POWERS OF COSINE AND SINE FUNCTIONS
Folia Mathematica Vol. 5, No., pp. 4 6 Acta Uiversitatis Lodziesis c 008 for Uiversity of Lódź Press SOME TRIGONOMETRIC IDENTITIES RELATED TO POWERS OF COSINE AND SINE FUNCTIONS ROMAN WITU LA, DAMIAN S
More informationSimilarity Solutions to Unsteady Pseudoplastic. Flow Near a Moving Wall
Iteratioal Mathematical Forum, Vol. 9, 04, o. 3, 465-475 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/0.988/imf.04.48 Similarity Solutios to Usteady Pseudoplastic Flow Near a Movig Wall W. Robi Egieerig
More informationConvergence of Random SP Iterative Scheme
Applied Mathematical Scieces, Vol. 7, 2013, o. 46, 2283-2293 HIKARI Ltd, www.m-hikari.com Covergece of Radom SP Iterative Scheme 1 Reu Chugh, 2 Satish Narwal ad 3 Vivek Kumar 1,2,3 Departmet of Mathematics,
More informationDirect Estimates for Lupaş-Durrmeyer Operators
Filomat 3:1 16, 191 199 DOI 1.98/FIL161191A Published by Faculty of Scieces ad Mathematics, Uiversity of Niš, Serbia Available at: http://www.pmf.i.ac.rs/filomat Direct Estimates for Lupaş-Durrmeyer Operators
More informationON SOME DIOPHANTINE EQUATIONS RELATED TO SQUARE TRIANGULAR AND BALANCING NUMBERS
Joural of Algebra, Number Theory: Advaces ad Applicatios Volume, Number, 00, Pages 7-89 ON SOME DIOPHANTINE EQUATIONS RELATED TO SQUARE TRIANGULAR AND BALANCING NUMBERS OLCAY KARAATLI ad REFİK KESKİN Departmet
More informationFixed Point Theorems for Expansive Mappings in G-metric Spaces
Turkish Joural of Aalysis ad Number Theory, 7, Vol. 5, No., 57-6 Available olie at http://pubs.sciepub.com/tjat/5//3 Sciece ad Educatio Publishig DOI:.69/tjat-5--3 Fixed Poit Theorems for Expasive Mappigs
More informationFLOOR AND ROOF FUNCTION ANALOGS OF THE BELL NUMBERS. H. W. Gould Department of Mathematics, West Virginia University, Morgantown, WV 26506, USA
INTEGERS: ELECTRONIC JOURNAL OF COMBINATORIAL NUMBER THEORY 7 (2007), #A58 FLOOR AND ROOF FUNCTION ANALOGS OF THE BELL NUMBERS H. W. Gould Departmet of Mathematics, West Virgiia Uiversity, Morgatow, WV
More informationAPPROXIMATION BY BERNSTEIN-CHLODOWSKY POLYNOMIALS
Hacettepe Joural of Mathematics ad Statistics Volume 32 (2003), 1 5 APPROXIMATION BY BERNSTEIN-CHLODOWSKY POLYNOMIALS E. İbili Received 27/06/2002 : Accepted 17/03/2003 Abstract The weighted approximatio
More informationGeneralization of Contraction Principle on G-Metric Spaces
Global Joural of Pure ad Applied Mathematics. ISSN 0973-1768 Volume 14, Number 9 2018), pp. 1159-1165 Research Idia Publicatios http://www.ripublicatio.com Geeralizatio of Cotractio Priciple o G-Metric
More informationA GRÜSS TYPE INEQUALITY FOR SEQUENCES OF VECTORS IN NORMED LINEAR SPACES AND APPLICATIONS
A GRÜSS TYPE INEQUALITY FOR SEQUENCES OF VECTORS IN NORMED LINEAR SPACES AND APPLICATIONS S. S. DRAGOMIR Abstract. A discrete iequality of Grüss type i ormed liear spaces ad applicatios for the discrete
More informationThe log-behavior of n p(n) and n p(n)/n
Ramauja J. 44 017, 81-99 The log-behavior of p ad p/ William Y.C. Che 1 ad Ke Y. Zheg 1 Ceter for Applied Mathematics Tiaji Uiversity Tiaji 0007, P. R. Chia Ceter for Combiatorics, LPMC Nakai Uivercity
More informationAMS Mathematics Subject Classification : 40A05, 40A99, 42A10. Key words and phrases : Harmonic series, Fourier series. 1.
J. Appl. Math. & Computig Vol. x 00y), No. z, pp. A RECURSION FOR ALERNAING HARMONIC SERIES ÁRPÁD BÉNYI Abstract. We preset a coveiet recursive formula for the sums of alteratig harmoic series of odd order.
More informationIntroductions to HarmonicNumber2
Itroductios to HarmoicNumber2 Itroductio to the differetiated gamma fuctios Geeral Almost simultaeously with the developmet of the mathematical theory of factorials, biomials, ad gamma fuctios i the 8th
More informationA Challenging Test For Convergence Accelerators: Summation Of A Series With A Special Sign Pattern
Applied Mathematics E-Notes, 6(006), 5-34 c ISSN 1607-510 Available free at mirror sites of http://www.math.thu.edu.tw/ ame/ A Challegig Test For Covergece Accelerators: Summatio Of A Series With A Special
More informationON BI-SHADOWING OF SUBCLASSES OF ALMOST CONTRACTIVE TYPE MAPPINGS
Vol. 9, No., pp. 3449-3453, Jue 015 Olie ISSN: 190-3853; Prit ISSN: 1715-9997 Available olie at www.cjpas.et ON BI-SHADOWING OF SUBCLASSES OF ALMOST CONTRACTIVE TYPE MAPPINGS Awar A. Al-Badareh Departmet
More informationarxiv: v2 [math.nt] 9 May 2017
arxiv:6.42v2 [math.nt] 9 May 27 Itegral Represetatios of Equally Positive Iteger-Idexed Harmoic Sums at Ifiity Li Jiu Research Istitute for Symbolic Computatio Johaes Kepler Uiversity 44 Liz, Austria ljiu@risc.ui-liz.ac.at
More informationBijective Proofs of Gould s and Rothe s Identities
ESI The Erwi Schrödiger Iteratioal Boltzmagasse 9 Istitute for Mathematical Physics A-1090 Wie, Austria Bijective Proofs of Gould s ad Rothe s Idetities Victor J. W. Guo Viea, Preprit ESI 2072 (2008 November
More informationOn a class of convergent sequences defined by integrals 1
Geeral Mathematics Vol. 4, No. 2 (26, 43 54 O a class of coverget sequeces defied by itegrals Dori Adrica ad Mihai Piticari Abstract The mai result shows that if g : [, ] R is a cotiuous fuctio such that
More informationJournal of Ramanujan Mathematical Society, Vol. 24, No. 2 (2009)
Joural of Ramaua Mathematical Society, Vol. 4, No. (009) 199-09. IWASAWA λ-invariants AND Γ-TRANSFORMS Aupam Saikia 1 ad Rupam Barma Abstract. I this paper we study a relatio betwee the λ-ivariats of a
More informationSubject: Differential Equations & Mathematical Modeling-III
Power Series Solutios of Differetial Equatios about Sigular poits Subject: Differetial Equatios & Mathematical Modelig-III Lesso: Power series solutios of differetial equatios about Sigular poits Lesso
More informationμ are complex parameters. Other
A New Numerical Itegrator for the Solutio of Iitial Value Problems i Ordiary Differetial Equatios. J. Suday * ad M.R. Odekule Departmet of Mathematical Scieces, Adamawa State Uiversity, Mubi, Nigeria.
More informationLOWER BOUNDS FOR THE BLOW-UP TIME OF NONLINEAR PARABOLIC PROBLEMS WITH ROBIN BOUNDARY CONDITIONS
Electroic Joural of Differetial Equatios, Vol. 214 214), No. 113, pp. 1 5. ISSN: 172-6691. URL: http://ejde.math.txstate.edu or http://ejde.math.ut.edu ftp ejde.math.txstate.edu LOWER BOUNDS FOR THE BLOW-UP
More informationOn some properties of digamma and polygamma functions
J. Math. Aal. Appl. 328 2007 452 465 www.elsevier.com/locate/jmaa O some properties of digamma ad polygamma fuctios Necdet Batir Departmet of Mathematics, Faculty of Arts ad Scieces, Yuzucu Yil Uiversity,
More informationResearch Article Nonexistence of Homoclinic Solutions for a Class of Discrete Hamiltonian Systems
Abstract ad Applied Aalysis Volume 203, Article ID 39868, 6 pages http://dx.doi.org/0.55/203/39868 Research Article Noexistece of Homocliic Solutios for a Class of Discrete Hamiltoia Systems Xiaopig Wag
More informationSome Oscillation Properties of Third Order Linear Neutral Delay Difference Equations
ISSN (e): 50 3005 Volume, 05 Issue, 07 July 05 Iteratioal Joural of Computatioal Egieerig Research (IJCER) Some Oscillatio Properties of Third Order Liear Neutral Delay Differece Equatios AGeorge Maria
More informationAn Interpolation Process on Laguerre Polynomial
Global Joural of Pure ad Applied Mathematics. ISSN 0973-1768 Volume 13, Number 10 (2017), pp. 7089-7099 Research Idia Publicatios http://www.ripublicatio.com A Iterpolatio Process o Laguerre Polyomial
More informationInternational Journal of Engineering Research and Generic Science (IJERGS) Available Online at
International Journal of Engineering Research and Generic Science (IJERGS) Available Online at www.ijergs.in Volume - 4, Issue - 6, November - December - 2018, Page No. 19-25 ISSN: 2455-1597 Fractional
More informationk-generalized FIBONACCI NUMBERS CLOSE TO THE FORM 2 a + 3 b + 5 c 1. Introduction
Acta Math. Uiv. Comeiaae Vol. LXXXVI, 2 (2017), pp. 279 286 279 k-generalized FIBONACCI NUMBERS CLOSE TO THE FORM 2 a + 3 b + 5 c N. IRMAK ad M. ALP Abstract. The k-geeralized Fiboacci sequece { F (k)
More informationA Study on Some Integer Sequences
It. J. Cotemp. Math. Scieces, Vol. 3, 008, o. 3, 03-09 A Study o Some Iteger Sequeces Serpil Halıcı Sakarya Uiversity, Departmet of Mathematics Esetepe Campus, Sakarya, Turkey shalici@sakarya.edu.tr Abstract.
More informationThe Arakawa-Kaneko Zeta Function
The Arakawa-Kaeko Zeta Fuctio Marc-Atoie Coppo ad Berard Cadelpergher Nice Sophia Atipolis Uiversity Laboratoire Jea Alexadre Dieudoé Parc Valrose F-0608 Nice Cedex 2 FRANCE Marc-Atoie.COPPO@uice.fr Berard.CANDELPERGHER@uice.fr
More informationSome Tauberian theorems for weighted means of bounded double sequences
A. Ştiiţ. Uiv. Al. I. Cuza Iaşi. Mat. N.S. Tomul LXIII, 207, f. Some Tauberia theorems for weighted meas of bouded double sequeces Cemal Bele Received: 22.XII.202 / Revised: 24.VII.203/ Accepted: 3.VII.203
More informationHARMONIC SERIES WITH POLYGAMMA FUNCTIONS OVIDIU FURDUI. 1. Introduction and the main results
Joural of Classical Aalysis Volume 8, Number 06, 3 30 doi:0.753/jca-08- HARMONIC SERIES WITH POLYGAMMA FUNCTIONS OVIDIU FURDUI Abstract. The paper is about evaluatig i closed form the followig classes
More informationA GENERALIZATION OF THE SYMMETRY BETWEEN COMPLETE AND ELEMENTARY SYMMETRIC FUNCTIONS. Mircea Merca
Idia J Pure Appl Math 45): 75-89 February 204 c Idia Natioal Sciece Academy A GENERALIZATION OF THE SYMMETRY BETWEEN COMPLETE AND ELEMENTARY SYMMETRIC FUNCTIONS Mircea Merca Departmet of Mathematics Uiversity
More informationPAijpam.eu ON DERIVATION OF RATIONAL SOLUTIONS OF BABBAGE S FUNCTIONAL EQUATION
Iteratioal Joural of Pure ad Applied Mathematics Volume 94 No. 204, 9-20 ISSN: 3-8080 (prited versio); ISSN: 34-3395 (o-lie versio) url: http://www.ijpam.eu doi: http://dx.doi.org/0.2732/ijpam.v94i.2 PAijpam.eu
More information-ORDER CONVERGENCE FOR FINDING SIMPLE ROOT OF A POLYNOMIAL EQUATION
NEW NEWTON-TYPE METHOD WITH k -ORDER CONVERGENCE FOR FINDING SIMPLE ROOT OF A POLYNOMIAL EQUATION R. Thukral Padé Research Cetre, 39 Deaswood Hill, Leeds West Yorkshire, LS7 JS, ENGLAND ABSTRACT The objective
More information