Inclusion and argument properties for certain subclasses of multivalent functions defined by the Dziok-Srivastava operator
|
|
- Joan Cobb
- 5 years ago
- Views:
Transcription
1 Advances in Theoretical Alied Mathematics. ISSN Volume 11, Number 4 016, Research India Publications htt:// Inclusion argument roerties for certain subclasses of multivalent functions defined by the Dziok-Srivastava oerator Jae Ho Choi Deartment of Mathematics Education, Daegu National University of Education, 19 Jungangdaero, Namgu, Daegu 4411, Korea. choijh@dnue.ac.kr Abstract The object of the resent aer is to investigate some inclusion relationshis argument roerties of several subclasses of multivalent analytic functions, which are defined here by using the Dziok-Srivastava oerator. Furthermore, relevant connections of the results resented in this aer with those obtained in earlier works are also ointed out. AMS subject classification: 30C45, 30C50. Keywords: Multivalent functions, Generalized hyergeometric function, Subordination, Hadamard roduct or convolution, Dziok-Srivastava oerator. 1. Introduction Definitions Let A denote the class of functions fzof the form fz= z + a +k z +k N := {1,, 3,...}, 1.1 k=1 which are analytic in the oen unit disk U ={z : z C z < 1}. Also let f g be analytic in U with f0 = g0. Then we say that f is subordinate to g in U, written f g or fz gz, if there exists the Schwarz function w, analytic in U such that w0 = 0, wz < 1 fz= gwz z U. We also observe that fz gz in U
2 36 Jae Ho Choi if only if f0 = g0 fu gu whenever g is univalent in U. Let M be the class of analytic functions ϕ with ϕ0 = 1, which are convex univalent in U for which Re{ϕz} > 0 z U. Making use of the aforementioned rincile of subordination between analytic functions, we define each of the following subclasses of A S {f η; ϕ := 1 zf } z : f A η fz η ϕz 1. ϕ M; 0 η<; z U { 1 K η; ϕ := f : f A η ϕ M; 0 η<; z U. 1 + zf } z f z η ϕz 1.3 We note that S η; 1 + z =: S 1 z K η; 1 + z =: K η 0 η<, 1 z where S η K ηdenote the subclasses of A consisting of all analytic functions which are valently starlike of order η in U valently convex of order η in U, resectively. For functions f j z A, given by f j z = z + a +k,j z +k k=1 j = 1, ; N, we define the Hadamard roduct or convolution of f 1 z f z by f 1 f z = z + a +k,1 a +k, z +k = f f 1 z k=1 N; z U. Let α i i = 1,...,l β j j = 1,...,mbe comlex numbers with β j / Z 0 := {0, 1,,...}. Then the generalized hyergeometric function l F m is defined by α 1 k α l k z k lf m α 1,...,α l ; β 1,...,β m ; z = β k=0 1 k β m k k! l m + 1; N 0 := N {0}; z U,
3 Inclusion argument roerties for certain subclasses 363 where λ k is the Pochhammer symbol defined, in terms of the Gamma function, by λ k = Ɣλ + k Ɣλ { 1 k = 0 = λλ + 1 λ + k 1 k N. Dziok Srivastava [1] considered a linear oerator H α 1,...,α l ; β 1,...,β m defined by the following Hadamard roduct: H α 1,...,α l ; β 1,...,β m f z := [z lf m α 1,...,α l ; β 1,...,β m ; z] f z l m + 1; N 0 ; z U. 1.4 Then it is observed that H α 1,...,α l ; β 1,...,β m also mas A onto itself as follows: H α 1,...,α l ; β 1,...,β m f z = z α 1 k α l k 1 + β k=1 1 k β m k k! a +kz +k 1.5 f A; z U. To make the notation simle, we write α 1f z := H α 1,...,α l ; β 1,...,β m f z. It is easily verified from 1.4 that z α 1f z = α1 α 1 + 1f z α 1 α 1f z f A. 1.6 It should be remarked that the linear oerator α 1 is a generalization of many other linear oerators considered earlier. In articular, for f A we obtain the following observations: i H 1 a, b; cf z = H a,b,c fza,c C; c/ Z 0, the linear oerator studied by Hohlov []. ii H n +, 1; 1f z = D n+ 1 fz n N; n >, the linear oerator investigated by Goel Sohi [3]. In the case when = 1, D n fz is the Ruscheweyh derivative [4]. Ɣ + 1 λ iii H + 1, 1; + 1 λf z = z λ Dz λ fz 0 λ<1, where Ɣ + 1 fzis the fractional derivative of fzof order λ cf. [5]; see also [6]. D λ z iv H a, 1; cf z = L a, cf z a R; c R \ Z 0, the linear oerator studied by Saito [7] which yields the oerator La, cf z introduced by Carlson Shaffer [8] for = 1.
4 364 Jae Ho Choi v H 1 µ, 1; λ + 1f z = I λ,µ f z λ > 1; µ>0, the oerator considered by Choi et al. [9]. vi H λ +, c; af z = I λ a, cf z a, c R \ Z 0 ; λ>, the Cho-Kwon- Srivastava oerator [10]. Now, by making use of the Dziok-Srivastava oerator α 1, we define some new subclasses of analytic functions in A as following: We also note that S α 1; η; ϕ := {f : f A α 1f z S η; ϕ} 1.7 ϕ M; 0 η<; l m + 1; N 0 ; z U K α 1; η; ϕ := {f : f A α 1f z K η; ϕ} 1.8 ϕ M; 0 η<; l m + 1; N 0 ; z U. fz K α 1; η; ϕ zf z S α 1; η; ϕ. 1.9 In articular, for 1 <B<A 1, we write S α 1 ; η; 1 + Az = S 1 + Bz α 1; η; A, B K α 1 ; η; 1 + Az 1 + Bz = K α 1; η; A, B. Furthermore, the subclass S α 1; η; A, B of A was investigated by Patel et al. [11]. In the resent aer, we investigate some inclusion relationshis argument roerties of functions belonging to the subclasses S α 1; η; ϕ K α 1; η; ϕby using the technique of differential subordination. Some interesting alications involving the Dziok-Srivastava oerator α 1, defined by 1.4, are also considered.. Inclusion roerties involving H α 1 The following results will be required in our investigation. Lemma.1. Eenigenburg et al. [1]. Let hz be convex univalent in U with h0 = 1 Re{βhz + ν} > 0 β, ν C. If z is analytic in U with 0 = 1, then z + z z βz + ν hz z U
5 Inclusion argument roerties for certain subclasses 365 imlies that z hz z U. Lemma.. Miller Mocanu [13]. Let hz be convex univalent in U wz be analytic in U with Re{wz} 0. If z is analytic in U 0 = h0, then imlies that z hz z U. z + wzz z hz z U Lemma.3. Cf., e.g., Takahashi Nunokawa [14]. Let z be analytic in U with 0 = 1 z = 0 for all z U. If there exist two oints z 1,z U such that π λ 1 = argz 1 < argz < argz = π λ.1 for some λ 1 λ λ 1,λ > 0 for all z z < z 1 = z, then z 1 z 1 λ1 + λ z z λ1 + λ = i m = i m, z 1 z. where m 1 b b = i tan π λ λ b 4 λ 1 + λ.3 Lemma.4. Lashin [15]. Let hz be analytic in U, with h0 = 1 hz = 0 z U. Further suose that λ, µ R + = 0, arg hz + µzh z π < λ + π tan 1 λµ λ > 0; µ>0,.4 then arg hz < π λ z U..5 We begin by roving the following theorem. Theorem.5. Let ϕ M α 1 > η. Then Proof. Let fz S S α 1 + 1; η; ϕ S α 1; η; ϕ. α 1 + 1; η; ϕ set z = 1 η zh α 1f z α 1 f z η, where z = 1+c 1 z+c z + is analytic in U z = 0 for all z U. Alying the identity 1.6, we have α α 1 + 1f z 1 = ηz + α 1 + η..6 α 1 f z
6 366 Jae Ho Choi By using the logarithmic differentiating on both side of.6, then simlifying, we obtain 1 zh α 1 + 1f z z z η η = z + z U. α 1 + 1f z ηz + α 1 + η Since ϕz M, α 1 > η fz S α 1 + 1; η; ϕ, from 1.7 we see that Re{ ηϕz + α 1 + η} > 0 z U z z z + ϕz z U..7 ηz + α 1 + η Then, by alying Lemma.1 to.7, it follows that z ϕz in U, so that fz S α 1; η; ϕ. This evidently comletes the roof of Theorem.5. Theorem.6. Let ϕ M α 1 > η. Then K α 1 + 1; η; ϕ K α 1; η; ϕ. Proof. By using 1.9 Theorem.5, we observe that fz K α 1 + 1; η; ϕ zf z S α 1 + 1; η; ϕ zf z S α 1; η; ϕ fz K α 1; η; ϕ, which comletes the roof of Theorem.6. Taking ϕz = 1 + Az/1 + Bz 1 <B<A 1 in Theorem.5, we get the following corollary: Corollary.7. Let 1 <B<A 1 α 1 > η. Then S α 1 + 1; η; A, B S α 1; η; A, B K α 1 + 1; η; A, B K α 1; η; A, B. 3. Argument roerties involving H α 1 Theorem 3.1. Let 0 <δ 1,δ 1, 1 <B<A 1 α 1 > η. Iff A satisfies the following inequality π zh δ 1 < arg α 1 + 1f z γ < π α 1 + 1gz δ
7 Inclusion argument roerties for certain subclasses 367 for some g S α 1 + 1; η; A, B. Then π λ 1 < arg zh α 1f z α 1 gz γ < π λ where λ 1 λ 0 <λ 1,λ 1 are the solution of the following equations: δ 1 = λ 1 + λ π tan λ 1 b cos π t η1+a 1+B + η + α b + λ 1 + λ 1 b sin π t 1 δ = λ + π tan 1 when b is given by.3 t 1 = π sin 1 Proof. Let η1+a 1+B + η + α 1 λ 1 + λ 1 b cos π t b + λ 1 + λ 1 b sin π t 1 ηa B η1 AB + η + α 1 1 B z = 1 γ zh α 1f z α 1 gz By using the identity 1.6, we readily have 1 zh α 1 + 1f z γ γ α 1 + 1gz = 1 z zh α 1f z + α 1 α 1f z γ α 1 gz + α 1 H α 1 gz = 1 γ = 1 γ zh. 3.3 γ. 3.4 γ α1 + 1z α 1f z + z α 1f z α 1 gz + α 1 H α 1 gz zh z α α f z H α 1 gz z α 1 gz α 1 gz + z α 1 f z α 1 gz + α 1 γ. Since gz S α 1+1; η; A, B, by corollary.7, we see that gz S α 1; η; A, B. Therefore, we get qz = 1 zh α 1gz η η 1 + Az α 1 gz 1 + Bz. 3.5 γ
8 368 Jae Ho Choi From 3.4 we obtain zh α 1f z α 1 gz = γz+ γ. 3.6 Differentiating both sides of 3.6 logarithmically, it follows from 3.5 that z α 1f z = ηqz + η 1 + γz z α 1 f z γz+ γ. 3.7 By virtue of , we have z H α 1f z α 1 gz = γz z + ηqz + η 1 γz+ γ. Comuting the above equations, then simlifying, we observe that 1 zh α 1 + 1f z z z γ γ = z + α 1 + 1gz ηqz + η + α Furthermore, from 3.5 we get 1 AB qz 1 B < A B 1 B 1 <B<A 1; z U. 3.9 Thus, by using 3.9, we obtain where η1 A +η+α 1 <ρ< 1 B ηqz + η + α 1 = ρe i πφ, η1 + A +η+α 1 t 1 <φ<t 1, 1 + B t 1 being given by 3.3. We note that z is analytic in U with 0 = 1. Let w = hz be the function which mas U onto the angular domain { w : π δ 1 < argw < π } δ with h0 = 1. Alying Lemma. for this function h with wz = 1 ηqz + η + α 1,
9 Inclusion argument roerties for certain subclasses 369 we see that Rez > 0 z U, hence z = 0 z U. If there exist two oints z 1,z U such that the condition.1 is satisfied, then by Lemma.3 we obtain. under the restriction.3. Hence we get z 1 z 1 arg z 1 + ηqz 1 + η + α 1 = π λ 1 + arg 1 i λ 1 + λ m ρe i πφ 1 π λ 1 tan 1 λ1 + λ m sin π 1 φ ρ + λ 1 + λ m cos π 1 φ π λ 1 tan 1 = π δ 1 η1+a 1+B + η + α 1 λ 1 + λ 1 b cos π t 1 1 b + λ 1 + λ 1 b sin π t 1 z z arg z + ηqz + η + α 1 π λ + tan 1 λ 1 + λ 1 b cos π t 1 η1+a 1+B + η + α 1 1 b + λ 1 + λ 1 b sin π t 1 = π δ, where we have used the inequality.3, δ 1,δ t 1 being given by 3.1, These obviously contradict the assumtion of Theorem 3.1. The roof of Theorem 3.1 is thus comleted. If we ut δ 1 = δ in Theorem 3.1, we easily obtain the following consequence. Corollary 3.. Let 0 <δ 1, 1 <B<A 1 α 1 > η. If f A satisfies the following inequality zh arg α 1 + 1f z γ α 1 + 1gz < π δ for some g S α 1 + 1; η; A, B, then arg zh α 1f z α 1 gz γ < π λ, where λ0 <λ 1 is the solution of the following equation: δ = λ + λ cos π π tan 1 t 1 η1+a 1+B + η + α 1 + λ sin π t 1
10 370 Jae Ho Choi when t 1 is given by 3.3. Finally, by alying Lemma.4, we rove the following roerties. Theorem 3.3. Let α 1 > 0 γ,λ,µ R +, let g A. Suose that f A satisfies the condition { H arg α } γ { 1f z H 1 + µ α 1 + 1f z α 1 gz H α } 1 + 1gz α 1 f z α 1 gz < π λ + [ ] λµ π tan 1, γα 1 then { H arg α } γ 1f z α 1 gz < π λ z U. Proof. If we set { H z = α } γ 1f z γ = 0, 3.10 α 1 gz then z is analytic in U, with 0 = 1 0 = 0. Making use of the logarithmic differentiation on both side of 3.10, we have 1 z z z γ z = H α 1f z α 1 f z By alying the identity 1.6 in 3.11, we obtain z + µ z z γα { 1 H = α } γ { 1f z 1 + µ α 1 gz Hence, by using Lemma.4, we conclude that z H H α 1 + 1f z α 1 f z α 1gz α 1 gz H α } 1 + 1gz. α 1 gz arg z < π λ z U, which comletes the roof of Theorem 3.3. Remark 3.4. Setting l = m + 1, µ = = 1, α i = β j = 1 i = 1,,...,m+ 1; j = 1,,...,m, gz = z in Theorem 3.3, we obtain the result due to Lashin [15], Theorem.6. Taking γ = 1 gz = z in Theorem 3.3, we have the following consequence.
11 Inclusion argument roerties for certain subclasses 371 Corollary 3.5. Let α 1 > 0 λ, µ R +. Suose that f A satisfies the condition { arg 1 µ H α 1f z z + µ H α } 1 + 1f z z < π λ + [ ] λµ π tan 1, α 1 then arg H α 1f z < π λ z z U. Theorem 3.6. Let α 1 > 0, 0 <µ 1 γ,λ R +. Suose that f A satisfies the condition H arg α 1f z z < π λ + [ ] µ π tan 1 λ z U. γα 1 then γα1 γα 1 z arg µ z µ t γα 1 µ+1 0 µ α 1f tdt < π λ. Proof. If we ut z = γα γα 1 1 z µ z µ t γα 1 µ+1 µ α 1f tdt, then z is analytic in U, with 0 = 1 0 = 0. By differentiating both sides of 3.1 with resect to z, we obtain z + µ z z = H α 1f z γα 1 z. Thus, in view of Lemma.4, we have arg z < π λ z U, which evidently roves Theorem 3.6. Remark 3.7. Taking l = m + 1, α i = β j = 1 i = 1,,...,m+ 1; j = 1,,...,m, γ = µ = = 1 in Theorem 3.6, we infer the result due to Goyal Goswami [16]. Furthermore, by secifying the arameters, α i i = 1,,...,l β j j = 1, 1,...,m, we obtain various results for different oerators reminded in the introduction. Acknowledgements This work was suorted by Daegu National University of Education Research grant in 015.
12 37 Jae Ho Choi References [1] J. Dziok H. M. Srivastava, Classes of analytic functions associated with generalized hyergeometric function, Math. Comut , [] Y. E. Hohlov, Convolution oerators reserving univalent functions, Ukr. Mat. Zh , 0 6 in Russian. [3] R. M. Goel N. S. Sohi, A new criterion for -valent functions, Proc. Amer. Math. Soc , [4] S. Ruscheweyh, New criteria for univalent functions, Proc. Amer. Math. Soc , [5] S. Owa, On the distortion theorems I, Kyungook Math. J , [6] S. Owa H. M. Srivastava, Univalent starlike generalized hyergeometric functions, Canad. J. Math , [7] H. Saitoh, A linear oerator its alications of first order differential subordinations, Math. Jaon , [8] B. C. Carlson D. B. Shaffer, Starlike restarlike hyergeometric functions, SIAM J. Math. Anal , [9] J. H. Choi, M. Saigo H. M. Srivastava, Some inclusion roerties of a certain family of integral oerators, J. Math. Anal. Al , [10] N. K. Cho, O. S. Kwon H. M. Srivastava, Inclusion relationshis argument roerties for certain subclasses of multivalent functions associated with a family of linear oerator, J. Math. Anal. Al , [11] J. Patel, A. K. Mishra H. M. Srivastava, Classes of multivalent analytic functions involving the Dziok-Srivastava oerator, Comut. Math. Al , [1] P. Eenigenburg, S. S. Miller, P. T. Mocanu M. O. Reade, On a Briot-Bouquet differential subordination, in General Inequalities 3, International Series of Numerical Mathematics, Vol. 64, Birkhäuser Verlag, Basel, 1983, [13] S. S. Miller P. T. Mocanu, Differential subordinations univalent functions, Michigan Math. J , [14] N. Takahashi M. Nunokawa, A certain connection between starlike convex functions, Al. Math. Lett , [15] A. Y. Lashin, Alications of Nunokawa s theorem, J. Inequal. Pure Al. Math , 1 5. Art [16] S.P. Goyal P. Goswami, Argument estimate of certain multivalent analytic functions defined by integral oerators, Tamsui Oxford J. Math. Sci ,
Differential Sandwich Theorem for Multivalent Meromorphic Functions associated with the Liu-Srivastava Operator
KYUNGPOOK Math. J. 512011, 217-232 DOI 10.5666/KMJ.2011.51.2.217 Differential Sandwich Theorem for Multivalent Meromorhic Functions associated with the Liu-Srivastava Oerator Rosihan M. Ali, R. Chandrashekar
More informationMajorization Properties for Subclass of Analytic p-valent Functions Defined by the Generalized Hypergeometric Function
Tamsui Oxford Journal of Information and Mathematical Sciences 284) 2012) 395-405 Aletheia University Majorization Properties for Subclass of Analytic p-valent Functions Defined by the Generalized Hypergeometric
More informationON CERTAIN CLASSES OF MULTIVALENT FUNCTIONS INVOLVING A GENERALIZED DIFFERENTIAL OPERATOR
Bull. Korean Math. Soc. 46 (2009), No. 5,. 905 915 DOI 10.4134/BKMS.2009.46.5.905 ON CERTAIN CLASSES OF MULTIVALENT FUNCTIONS INVOLVING A GENERALIZED DIFFERENTIAL OPERATOR Chellian Selvaraj and Kuathai
More informationNEW SUBCLASS OF MULTIVALENT HYPERGEOMETRIC MEROMORPHIC FUNCTIONS
Kragujevac Journal of Mathematics Volume 42(1) (2018), Pages 83 95. NEW SUBCLASS OF MULTIVALENT HYPERGEOMETRIC MEROMORPHIC FUNCTIONS M. ALBEHBAH 1 AND M. DARUS 2 Abstract. In this aer, we introduce a new
More informationSufficient conditions for certain subclasses of meromorphic p-valent functions
Bol. Soc. Paran. Mat. (3s.) v. 33 (015): 9 16. c SPM ISSN-175-1188 on line ISSN-0037871 in ress SPM: www.sm.uem.br/bsm doi:10.569/bsm.v33i.1919 Sufficient conditions for certain subclasses of meromorhic
More informationBulletin of the Transilvania University of Braşov Vol 8(57), No Series III: Mathematics, Informatics, Physics, 1-12
Bulletin of the Transilvania University of Braşov Vol 857), No. 2-2015 Series III: Mathematics, Informatics, Physics, 1-12 DISTORTION BOUNDS FOR A NEW SUBCLASS OF ANALYTIC FUNCTIONS AND THEIR PARTIAL SUMS
More informationDifferential Subordination and Superordination Results for Certain Subclasses of Analytic Functions by the Technique of Admissible Functions
Filomat 28:10 (2014), 2009 2026 DOI 10.2298/FIL1410009J Published by Faculty of Sciences and Mathematics, University of Niš, Serbia Available at: htt://www.mf.ni.ac.rs/filomat Differential Subordination
More informationA Certain Subclass of Multivalent Analytic Functions Defined by Fractional Calculus Operator
British Journal of Mathematics & Comuter Science 4(3): 43-45 4 SCIENCEDOMAIN international www.sciencedomain.org A Certain Subclass of Multivalent Analytic Functions Defined by Fractional Calculus Oerator
More informationSOME CLASSES OF MEROMORPHIC MULTIVALENT FUNCTIONS WITH POSITIVE COEFFICIENTS INVOLVING CERTAIN LINEAR OPERATOR
International Journal of Basic & Alied Sciences IJBAS-IJENS Vol:13 No:03 56 SOME CLASSES OF MEROMORPHIC MULTIVALENT FUNCTIONS WITH POSITIVE COEFFICIENTS INVOLVING CERTAIN LINEAR OPERATOR Abdul Rahman S
More informationMalaya J. Mat. 4(1)(2016) 37-41
Malaya J. Mat. 4(1)(2016) 37-41 Certain coefficient inequalities for -valent functions Rahim Kargar a,, Ali Ebadian a and Janus Sokół b a Deartment of Mathematics, Payame Noor University, I. R. of Iran.
More informationResearch Article On a New Class of p-valent Meromorphic Functions Defined in Conic Domains
e Scientific World Journal Volume 2016, Article ID 6360250, 7 ages htt://dx.doi.org/10.1155/2016/6360250 Research Article On a New Class of -Valent Meromorhic Functions Defined in Conic Domains Mohammed
More informationConvolution properties for subclasses of meromorphic univalent functions of complex order. Teodor Bulboacă, Mohamed K. Aouf, Rabha M.
Faculty of Sciences Mathematics, University of Niš, Serbia Available at: http://www.pmf.ni.ac.rs/filomat Filomat 26:1 (2012), 153 163 DOI: 10.2298/FIL1201153B Convolution properties for subclasses of meromorphic
More informationSOME CRITERIA FOR STRONGLY STARLIKE MULTIVALENT FUNCTIONS
Bulletin of the Institute of Mathematics Academia Sinica (New Series) Vol. 7 (01), No. 3, pp. 43-436 SOME CRITERIA FOR STRONGLY STARLIKE MULTIVALENT FUNCTIONS DINGGONG YANG 1 AND NENG XU,b 1 Department
More informationInclusion relationships for certain classes of analytic functions involving the Choi-Saigo-Srivastava operator
Cho Yoon Journal of Inequalities Applications 2013, 2013:83 R E S E A R C H Open Access Inclusion relationships for certain classes of analytic functions involving the Choi-Saigo-Srivastava operator Nak
More informationCoefficient bounds for some subclasses of p-valently starlike functions
doi: 0.2478/v0062-02-0032-y ANNALES UNIVERSITATIS MARIAE CURIE-SKŁODOWSKA LUBLIN POLONIA VOL. LXVII, NO. 2, 203 SECTIO A 65 78 C. SELVARAJ, O. S. BABU G. MURUGUSUNDARAMOORTHY Coefficient bounds for some
More informationOn Certain Properties of Neighborhoods of. Dziok-Srivastava Differential Operator
International Matheatical Foru, Vol. 6, 20, no. 65, 3235-3244 On Certain Proerties of Neighborhoods of -Valent Functions Involving a Generalized Dziok-Srivastava Differential Oerator Hesa Mahzoon Deartent
More informationSUBORDINATION RESULTS FOR CERTAIN SUBCLASSES OF UNIVALENT MEROMORPHIC FUNCTIONS
SUBORDINATION RESULTS FOR CERTAIN SUBCLASSES OF UNIVALENT MEROMORPHIC FUNCTIONS, P.G. Student, Department of Mathematics,Science College, Salahaddin University, Erbil, Region of Kurdistan, Abstract: In
More informationConvolution Properties for Certain Meromorphically Multivalent Functions
Filomat 31:1 (2017), 113 123 DOI 10.2298/FIL1701113L Published by Faculty of Sciences and Mathematics, University of Niš, Serbia Available at: htt://www.mf.ni.ac.rs/filomat Convolution Proerties for Certain
More informationJournal of Inequalities in Pure and Applied Mathematics
Journal of Inequalities in Pure and Applied Mathematics APPLICATIONS OF DIFFERENTIAL SUBORDINATION TO CERTAIN SUBCLASSES OF MEROMORPHICALLY MULTIVALENT FUNCTIONS H.M. SRIVASTAVA AND J. PATEL Department
More informationSubclass of Meromorphic Functions with Positive Coefficients Defined by Frasin and Darus Operator
Int. J. Open Problems Complex Analysis, Vol. 8, No. 1, March 2016 ISSN 2074-2827; Copyright c ICSRS Publication, 2016 www.i-csrs.org Subclass of Meromorphic Functions with Positive Coefficients Defined
More informationON A DIFFERENTIAL SUBORDINATION AND SUPERORDINATION OF NEW CLASS OF MEROMORPHIC FUNCTIONS
LE MATEMATICHE Vol. LXIX 2014) Fasc. I, pp. 259 274 doi: 10.4418/2014.69.1.20 ON A DIFFERENTIAL SUBORDINATION AND SUPERORDINATION OF NEW CLASS OF MEROMORPHIC FUNCTIONS ALI MUHAMMAD - MARJAN SAEED In this
More informationSTRONG DIFFERENTIAL SUBORDINATION AND SUPERORDINATION OF NEW GENERALIZED DERIVATIVE OPERATOR. Anessa Oshah and Maslina Darus
Korean J. Math. 23 2015, No. 4, pp. 503 519 http://dx.doi.org/10.11568/jm.2015.23.4.503 STRONG DIFFERENTIAL SUBORDINATION AND SUPERORDINATION OF NEW GENERALIZED DERIVATIVE OPERATOR Anessa Oshah and Maslina
More informationOn a New Subclass of Meromorphically Multivalent Functions Defined by Linear Operator
International Mathematical Forum, Vol. 8, 213, no. 15, 713-726 HIKARI Ltd, www.m-hikari.com On a New Subclass of Meromorphically Multivalent Functions Defined by Linear Operator Ali Hussein Battor, Waggas
More informationCoefficient inequalities for certain subclasses Of p-valent functions
Coefficient inequalities for certain subclasses Of -valent functions R.B. Sharma and K. Saroja* Deartment of Mathematics, Kakatiya University, Warangal, Andhra Pradesh - 506009, India. rbsharma_005@yahoo.co.in
More informationInclusion and Argument Properties for Certain Subclasses of Analytic Functions Defined by Using on Extended Multiplier Transformations
Advances in Pure Matheatics, 0,, 93-00 doi:0.436/a.0.4034 Pubished Onine Juy 0 (htt://www.scirp.org/journa/a) Incusion Arguent Proerties for Certain Subcasses of Anaytic Functions Defined by Using on Extended
More informationA NEW CLASS OF MEROMORPHIC FUNCTIONS RELATED TO CHO-KWON-SRIVASTAVA OPERATOR. F. Ghanim and M. Darus. 1. Introduction
MATEMATIQKI VESNIK 66, 1 14, 9 18 March 14 originalni nauqni rad research paper A NEW CLASS OF MEROMORPHIC FUNCTIONS RELATED TO CHO-KWON-SRIVASTAVA OPERATOR F. Ghanim and M. Darus Abstract. In the present
More informationSubclass Of K Uniformly Starlike Functions Associated With Wright Generalized Hypergeometric Functions
P a g e 52 Vol.10 Issue 5(Ver 1.0)September 2010 Subclass Of K Uniformly Starlike Functions Associated With Wright Generalized Hypergeometric Functions G.Murugusundaramoorthy 1, T.Rosy 2 And K.Muthunagai
More informationSOME INCLUSION PROPERTIES OF STARLIKE AND CONVEX FUNCTIONS ASSOCIATED WITH HOHLOV OPERATOR. II
italian journal of pure and applied mathematics n. 37 2017 117 126 117 SOME INCLUSION PROPERTIES OF STARLIKE AND CONVEX FUNCTIONS ASSOCIATED WITH HOHLOV OPERATOR. II M. Kasthuri K. Vijaya 1 K. Uma School
More informationDIFFERENTIAL SUBORDINATION RESULTS FOR NEW CLASSES OF THE FAMILY E(Φ, Ψ)
DIFFERENTIAL SUBORDINATION RESULTS FOR NEW CLASSES OF THE FAMILY E(Φ, Ψ) Received: 05 July, 2008 RABHA W. IBRAHIM AND MASLINA DARUS School of Mathematical Sciences Faculty of Science and Technology Universiti
More informationSOME SUBCLASSES OF ANALYTIC FUNCTIONS DEFINED BY GENERALIZED DIFFERENTIAL OPERATOR. Maslina Darus and Imran Faisal
Acta Universitatis Apulensis ISSN: 1582-5329 No. 29/212 pp. 197-215 SOME SUBCLASSES OF ANALYTIC FUNCTIONS DEFINED BY GENERALIZED DIFFERENTIAL OPERATOR Maslina Darus and Imran Faisal Abstract. Let A denote
More informationMajorization for Certain Classes of Meromorphic Functions Defined by Integral Operator
Int. J. Open Problems Complex Analysis, Vol. 5, No. 3, November, 2013 ISSN 2074-2827; Copyright c ICSRS Publication, 2013 www.i-csrs.org Majorization for Certain Classes of Meromorphic Functions Defined
More informationA. Then p P( ) if and only if there exists w Ω such that p(z)= (z U). (1.4)
American International Journal of Research in Science, Technology, Engineering & Mathematics Available online at http://www.iasir.net ISSN (Print): 2328-3491, ISSN (Online): 2328-3580, ISSN (CD-ROM): 2328-3629
More informationTHE FEKETE-SZEGÖ COEFFICIENT FUNCTIONAL FOR TRANSFORMS OF ANALYTIC FUNCTIONS. Communicated by Mohammad Sal Moslehian. 1.
Bulletin of the Iranian Mathematical Society Vol. 35 No. (009 ), pp 119-14. THE FEKETE-SZEGÖ COEFFICIENT FUNCTIONAL FOR TRANSFORMS OF ANALYTIC FUNCTIONS R.M. ALI, S.K. LEE, V. RAVICHANDRAN AND S. SUPRAMANIAM
More informationSUBORDINATION AND SUPERORDINATION FOR FUNCTIONS BASED ON DZIOK-SRIVASTAVA LINEAR OPERATOR
Bulletin of Mathematical Analysis and Applications ISSN: 1821-1291, URL: http://www.bmathaa.org Volume 2, Issue 3(21), Pages 15-26. SUBORDINATION AND SUPERORDINATION FOR FUNCTIONS BASED ON DZIOK-SRIVASTAVA
More informationSome Geometric Properties of a Certain Subclass of Univalent Functions Defined by Differential Subordination Property
Gen. Math. Notes Vol. 20 No. 2 February 2014 pp. 79-94 SSN 2219-7184; Copyright CSRS Publication 2014 www.i-csrs.org Available free online at http://www.geman.in Some Geometric Properties of a Certain
More informationMULTIVALENTLY MEROMORPHIC FUNCTIONS ASSOCIATED WITH CONVOLUTION STRUCTURE. Kaliyapan Vijaya, Gangadharan Murugusundaramoorthy and Perumal Kathiravan
Acta Universitatis Apulensis ISSN: 1582-5329 No. 30/2012 pp. 247-263 MULTIVALENTLY MEROMORPHIC FUNCTIONS ASSOCIATED WITH CONVOLUTION STRUCTURE Kaliyapan Vijaya, Gangadharan Murugusundaramoorthy and Perumal
More informationGENERALIZATIONS OF STRONGLY STARLIKE FUNCTIONS. Jacek Dziok 1. INTRODUCTION. a n z n (z U). dm (t) k. dm (t) =2,
TAIWANESE JOURNAL OF MATHEMATICS Vol. 18, No. 1, pp. 39-51, February 14 DOI: 1.1165/tjm.18.14.986 This paper is available online at http://journal.taiwanmathsoc.org.tw GENERALIZATIONS OF STRONGLY STARLIKE
More informationOn Certain Class of Meromorphically Multivalent Reciprocal Starlike Functions Associated with the Liu-Srivastava Operator Defined by Subordination
Filomat 8:9 014, 1965 198 DOI 10.98/FIL1409965M Published by Faculty of Sciences and Mathematics, University of Niš, Serbia Available at: http://www.pmf.ni.ac.rs/filomat On Certain Class of Meromorphically
More informationQuasiHadamardProductofCertainStarlikeandConvexPValentFunctions
Global Journal of Science Frontier Research: F Mathematics and Decision Sciences Volume 8 Issue Version.0 Year 208 Tye: Double Blind Peer Reviewed International Research Journal Publisher: Global Journals
More informationFekete-Szegö Inequality for Certain Classes of Analytic Functions Associated with Srivastava-Attiya Integral Operator
Applied Mathematical Sciences, Vol. 9, 015, no. 68, 3357-3369 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.1988/ams.015.543 Fekete-Szegö Inequality for Certain Classes of Analytic Functions Associated
More informationA New Subclasses of Meromorphic p-valent Functions with Positive Coefficient Defined by Fractional Calculus Operators
Volume 119 No. 15 2018, 2447-2461 ISSN: 1314-3395 (on-line version) url: http://www.acadpubl.eu/hub/ http://www.acadpubl.eu/hub/ A New Subclasses of Meromorphic p-valent Functions with Positive Coefficient
More informationConvex Functions and Functions with Bounded Turning
Tamsui Oxford Journal of Mathematical Sciences 26(2) (2010) 161-172 Aletheia University Convex Functions Functions with Bounded Turning Nikola Tuneski Faculty of Mechanical Engineering, Karpoš II bb, 1000
More informationCertain properties of a new subclass of close-to-convex functions
Arab J Math (212) 1:39 317 DOI 1.17/s465-12-29-y RESEARCH ARTICLE Pranay Goswami Serap Bulut Teodor Bulboacă Certain properties of a new subclass of close-to-convex functions Received: 18 November 211
More informationA New Criterion for Meromorphic Multivalent Starlike Functions of Order γ defined by Dziok and Srivastava Operator
Proceeding of the Paitan Academy of Science 5 :77 83 3 Coyright Paitan Academy of Science ISSN: 377-969 rint 36-448 online Paitan Academy of Science Reearch Article A New Criterion for Meromorhic Multivalent
More informationA subclass of analytic functions
Stud. Univ. Babeş-Bolyai Math. 57(2012), No. 2, 277 282 A subclass of analytic functions Andreea-Elena Tudor Abstract. In the present paper, by means of Carlson-Shaffer operator and a multiplier transformation,
More informationSubordination and Superordination Results for Analytic Functions Associated With Convolution Structure
Int. J. Open Problems Complex Analysis, Vol. 2, No. 2, July 2010 ISSN 2074-2827; Copyright c ICSRS Publication, 2010 www.i-csrs.org Subordination and Superordination Results for Analytic Functions Associated
More informationRosihan M. Ali and V. Ravichandran 1. INTRODUCTION
TAIWANESE JOURNAL OF MATHEMATICS Vol. 14, No. 4, pp. 1479-1490, August 2010 This paper is available online at http://www.tjm.nsysu.edu.tw/ CLASSES OF MEROMORPHIC α-convex FUNCTIONS Rosihan M. Ali and V.
More informationSubordinate Solutions of a Differential Equation
Subordinate Solutions of a Differential Equation Stacey Muir Abstract In 2003, Ruscheweyh and Suffridge settled a conjecture of Pólya and Schoenberg on subordination of the de la Vallée Poussin means of
More informationON THE FEKETE-SZEGÖ INEQUALITY FOR A CLASS OF ANALYTIC FUNCTIONS DEFINED BY USING GENERALIZED DIFFERENTIAL OPERATOR
Acta Universitatis Apulensis ISSN: 58-539 No. 6/0 pp. 67-78 ON THE FEKETE-SZEGÖ INEQUALITY FOR A CLASS OF ANALYTIC FUNCTIONS DEFINED BY USING GENERALIZED DIFFERENTIAL OPERATOR Salma Faraj Ramadan, Maslina
More informationDifferential Operator of a Class of Meromorphic Univalent Functions With Negative Coefficients
Differential Operator of a Class of Meromorphic Univalent Functions With Negative Coefficients Waggas Galib Atshan and Ali Hamza Abada Department of Mathematics College of Computer Science and Mathematics
More informationThe Noor Integral and Strongly Starlike Functions
Journal of Mathematical Analysis and Applications 61, 441 447 (001) doi:10.1006/jmaa.001.7489, available online at http://www.idealibrary.com on The Noor Integral and Strongly Starlike Functions Jinlin
More informationOn Multivalent Functions Associated with Fixed Second Coefficient and the Principle of Subordination
International Journal of Mathematical Analysis Vol. 9, 015, no. 18, 883-895 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.1988/ijma.015.538 On Multivalent Functions Associated with Fixed Second Coefficient
More informationOn Quasi-Hadamard Product of Certain Classes of Analytic Functions
Bulletin of Mathematical analysis Applications ISSN: 1821-1291, URL: http://www.bmathaa.org Volume 1, Issue 2, (2009), Pages 36-46 On Quasi-Hadamard Product of Certain Classes of Analytic Functions Wei-Ping
More informationDIFFERENTIAL SANDWICH THEOREMS FOR SOME SUBCLASSES OF ANALYTIC FUNCTIONS INVOLVING A LINEAR OPERATOR. 1. Introduction
DIFFERENTIAL SANDWICH THEOREMS FOR SOME SUBCLASSES OF ANALYTIC FUNCTIONS INVOLVING A LINEAR OPERATOR T. N. SHAMMUGAM, C. RAMACHANDRAN, M. DARUS S. SIVASUBRAMANIAN Abstract. By making use of the familiar
More informationTwo Points-Distortion Theorems for Multivalued Starlike Functions
Int. Journal of Math. Analysis, Vol. 2, 2008, no. 17, 799-806 Two Points-Distortion Theorems for Multivalued Starlike Functions Yaşar Polato glu Department of Mathematics and Computer Science TC İstanbul
More informationDIFFERENTIAL SANDWICH THEOREMS FOR SOME SUBCLASSES OF ANALYTIC FUNCTIONS INVOLVING A LINEAR OPERATOR. 1. Introduction
Acta Math. Univ. Comenianae Vol. LXXVI, 2(2007), pp. 287 294 287 DIFFERENTIAL SANDWICH THEOREMS FOR SOME SUBCLASSES OF ANALYTIC FUNCTIONS INVOLVING A LINEAR OPERATOR T. N. SHAMMUGAM, C. RAMACHANDRAN, M.
More informationSANDWICH-TYPE THEOREMS FOR A CLASS OF INTEGRAL OPERATORS ASSOCIATED WITH MEROMORPHIC FUNCTIONS
East Asian Mathematical Journal Vol. 28 (2012), No. 3, pp. 321 332 SANDWICH-TYPE THEOREMS FOR A CLASS OF INTEGRAL OPERATORS ASSOCIATED WITH MEROMORPHIC FUNCTIONS Nak Eun Cho Abstract. The purpose of the
More informationResearch Article Some Properties of Certain Integral Operators on New Subclasses of Analytic Functions with Complex Order
Alied Mathematics Volume 2012, Article ID 161436, 9 ages doi:10.1155/2012/161436 esearch Article Some Proerties of Certain Integral Oerators on New Subclasses of Analytic Functions with Comlex Order Aabed
More informationA NOVEL SUBCLASS OF UNIVALENT FUNCTIONS INVOLVING OPERATORS OF FRACTIONAL CALCULUS P.N. Kamble 1, M.G. Shrigan 2, H.M.
International Journal of Applied Mathematics Volume 30 No. 6 2017, 501-514 ISSN: 1311-1728 printed version; ISSN: 1314-8060 on-line version doi: http://dx.doi.org/10.12732/ijam.v30i6.4 A NOVEL SUBCLASS
More informationSome basic properties of certain subclasses of meromorphically starlike functions
Wang et al. Journal of Inequalities Applications 2014, 2014:29 R E S E A R C H Open Access Some basic properties of certain subclasses of meromorphically starlike functions Zhi-Gang Wang 1*, HM Srivastava
More informationA NEW SUBCLASS OF MEROMORPHIC FUNCTION WITH POSITIVE COEFFICIENTS
Bulletin of Mathematical Analysis and Applications ISSN: 1821-1291, URL: http://www.bmathaa.org Volume 3 Issue 32010), Pages 109-121. A NEW SUBCLASS OF MEROMORPHIC FUNCTION WITH POSITIVE COEFFICIENTS S.
More informationResearch Article A Study of Cho-Kwon-Srivastava Operator with Applications to Generalized Hypergeometric Functions
International Mathematics and Mathematical Sciences, Article ID 374821, 6 pages http://dx.doi.org/10.1155/2014/374821 Research Article A Study of Cho-Kwon-Srivastava Operator with Applications to Generalized
More informationRIEMANN-STIELTJES OPERATORS BETWEEN WEIGHTED BERGMAN SPACES
RIEMANN-STIELTJES OPERATORS BETWEEN WEIGHTED BERGMAN SPACES JIE XIAO This aer is dedicated to the memory of Nikolaos Danikas 1947-2004) Abstract. This note comletely describes the bounded or comact Riemann-
More informationj(z) > + FZ f(z) z + oz f(z) 1-.F < 1-.F zf (z) } 1 E (z 6 U,F 1). (1.3) >/(z e u) ANGULAR ESTIMATIONS OF CERTAIN INTEGRAL OPERATORS
Internat. J. Math. & Math. Sci. VOL. 1 NO. (1998) 369374 369 ANGULAR ESTIMATIONS OF CERTAIN INTEGRAL OPERATORS NAK EUN CHO, IN HWA KIM JI A KIM Department of Applied Mathematics Pukyong National University
More informationSOME PROPERTIES OF A SUBCLASS OF ANALYTIC FUNCTIONS DEFINED BY A GENERALIZED SRIVASTAVA-ATTIYA OPERATOR. Nagat. M. Mustafa and Maslina Darus
FACTA UNIVERSITATIS NIŠ) Ser. Math. Inform. Vol. 27 No 3 2012), 309 320 SOME PROPERTIES OF A SUBCLASS OF ANALYTIC FUNCTIONS DEFINED BY A GENERALIZED SRIVASTAVA-ATTIYA OPERATOR Nagat. M. Mustafa and Maslina
More informationSufficient conditions for starlike functions associated with the lemniscate of Bernoulli
Kumar et al. Journal of Inequalities and Applications 2013, 2013:176 R E S E A R C H Open Access Sufficient conditions for starlike functions associated with the lemniscate of Bernoulli S Sivaprasad Kumar
More informationAbstract. For the Briot-Bouquet differential equations of the form given in [1] zu (z) u(z) = h(z),
J. Korean Math. Soc. 43 (2006), No. 2, pp. 311 322 STRONG DIFFERENTIAL SUBORDINATION AND APPLICATIONS TO UNIVALENCY CONDITIONS José A. Antonino Astract. For the Briot-Bouquet differential equations of
More informationRosihan M. Ali, M. Hussain Khan, V. Ravichandran, and K. G. Subramanian. Let A(p, m) be the class of all p-valent analytic functions f(z) = z p +
Bull Korean Math Soc 43 2006, No 1, pp 179 188 A CLASS OF MULTIVALENT FUNCTIONS WITH NEGATIVE COEFFICIENTS DEFINED BY CONVOLUTION Rosihan M Ali, M Hussain Khan, V Ravichandran, and K G Subramanian Abstract
More informationDifferential subordination theorems for new classes of meromorphic multivalent Quasi-Convex functions and some applications
Int. J. Adv. Appl. Math. and Mech. 2(3) (2015) 126-133 (ISSN: 2347-2529) Journal homepage: www.ijaamm.com International Journal of Advances in Applied Mathematics and Mechanics Differential subordination
More informationProducts of Composition, Multiplication and Differentiation between Hardy Spaces and Weighted Growth Spaces of the Upper-Half Plane
Global Journal of Pure and Alied Mathematics. ISSN 0973-768 Volume 3, Number 9 (207),. 6303-636 Research India Publications htt://www.riublication.com Products of Comosition, Multilication and Differentiation
More informationAN EXTENSION OF THE REGION OF VARIABILITY OF A SUBCLASS OF UNIVALENT FUNCTIONS
AN EXTENSION OF THE REGION OF VARIABILITY OF A SUBCLASS OF UNIVALENT FUNCTIONS SUKHWINDER SINGH SUSHMA GUPTA AND SUKHJIT SINGH Department of Applied Sciences Department of Mathematics B.B.S.B. Engineering
More informationResearch Article A New Class of Meromorphically Analytic Functions with Applications to the Generalized Hypergeometric Functions
Abstract and Applied Analysis Volume 20, Article ID 59405, 0 pages doi:0.55/20/59405 Research Article A New Class of Meromorphically Analytic Functions with Applications to the Generalized Hypergeometric
More informationOn Starlike and Convex Functions with Respect to 2k-Symmetric Conjugate Points
Tamsui Oxford Journal of Mathematical Sciences 24(3) (28) 277-287 Aletheia University On Starlike and Convex Functions with espect to 2k-Symmetric Conjugate Points Zhi-Gang Wang and Chun-Yi Gao College
More informationON JOINT CONVEXITY AND CONCAVITY OF SOME KNOWN TRACE FUNCTIONS
ON JOINT CONVEXITY ND CONCVITY OF SOME KNOWN TRCE FUNCTIONS MOHMMD GHER GHEMI, NHID GHRKHNLU and YOEL JE CHO Communicated by Dan Timotin In this aer, we rovide a new and simle roof for joint convexity
More informationDIFFERENTIAL SUBORDINATION AND SUPERORDINATION OF ANALYTIC FUNCTIONS DEFINED BY THE MULTIPLIER TRANSFORMATION
M athematical I nequalities & A pplications Volume 12, Number 1 2009), 123 139 DIFFERENTIAL SUBORDINATION AND SUPERORDINATION OF ANALYTIC FUNCTIONS DEFINED BY THE MULTIPLIER TRANSFORMATION ROSIHAN M. ALI,
More informationA note on a subclass of analytic functions defined by a generalized Sălăgean and Ruscheweyh operator
General Mathematics Vol. 17, No. 4 (2009), 75 81 A note on a subclass of analytic functions defined by a generalized Sălăgean and Ruscheweyh operator Alina Alb Lupaş, Adriana Cătaş Abstract By means of
More informationFactorizations Of Functions In H p (T n ) Takahiko Nakazi
Factorizations Of Functions In H (T n ) By Takahiko Nakazi * This research was artially suorted by Grant-in-Aid for Scientific Research, Ministry of Education of Jaan 2000 Mathematics Subject Classification
More informationON CERTAIN CLASSES OF UNIVALENT MEROMORPHIC FUNCTIONS ASSOCIATED WITH INTEGRAL OPERATORS
TWMS J. App. Eng. Math. V.4, No.1, 214, pp. 45-49. ON CERTAIN CLASSES OF UNIVALENT MEROMORPHIC FUNCTIONS ASSOCIATED WITH INTEGRAL OPERATORS F. GHANIM 1 Abstract. This paper illustrates how some inclusion
More informationOn products of multivalent close-to-star functions
Arif et al. Journal of Inequalities and Alications 2015, 2015:5 R E S E A R C H Oen Access On roducts of multivalent close-to-star functions Muhammad Arif 1,JacekDiok 2*,MohsanRaa 3 and Janus Sokół 4 *
More informationA SUBORDINATION THEOREM WITH APPLICATIONS TO ANALYTIC FUNCTIONS
Bulletin of Mathematical Analysis and Applications ISSN: 1821-1291, URL: http://www.bmathaa.org Volume 3 Issue 3(2011, Pages 1-8. A SUBORDINATION THEOREM WITH APPLICATIONS TO ANALYTIC FUNCTIONS (COMMUNICATED
More informationPROPERTIES AND CHARACTERISTICS OF A FAMILY CONSISTING OF BAZILEVIĆ (TYPE) FUNCTIONS SPECIFIED BY CERTAIN LINEAR OPERATORS
Electronic Journal of Mathematical Analysis and Applications Vol. 7) July 019, pp. 39-47. ISSN: 090-79X online) http://math-frac.org/journals/ejmaa/ PROPERTIES AND CHARACTERISTICS OF A FAMILY CONSISTING
More informationGENERALIZED NORMS INEQUALITIES FOR ABSOLUTE VALUE OPERATORS
International Journal of Analysis Alications ISSN 9-8639 Volume 5, Number (04), -9 htt://www.etamaths.com GENERALIZED NORMS INEQUALITIES FOR ABSOLUTE VALUE OPERATORS ILYAS ALI, HU YANG, ABDUL SHAKOOR Abstract.
More informationCoecient bounds for certain subclasses of analytic functions of complex order
Hacettepe Journal of Mathematics and Statistics Volume 45 (4) (2016), 1015 1022 Coecient bounds for certain subclasses of analytic functions of complex order Serap Bulut Abstract In this paper, we introduce
More informationDIFFERENTIAL OPERATOR GENERALIZED BY FRACTIONAL DERIVATIVES
Miskolc Mathematical Notes HU e-issn 1787-2413 Vol. 12 (2011), No. 2, pp. 167 184 DIFFERENTIAL OPERATOR GENERALIZED BY FRACTIONAL DERIVATIVES RABHA W. IBRAHIM AND M. DARUS Received March 30, 2010 Abstract.
More informationORDER. 1. INTRODUCTION Let A denote the class of functions of the form
SARAJEVO JOURNAL OF MATHEMATICS Vol.10 (22) (2014), 55 60 DOI: 10.5644/SJM.10.1.07 ON UNIFIED CLASS OF γ-spirallike FUNCTIONS OF COMPLEX ORDER T. M. SEOUDY ABSTRACT. In this paper, we obtain a necessary
More informationSome Further Properties for Analytic Functions. with Varying Argument Defined by. Hadamard Products
International Mathematical Forum, Vol. 10, 2015, no. 2, 75-93 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/imf.2015.412205 Some Further Properties for Analytic Functions with Varying Argument
More informationOn neighborhoods of functions associated with conic domains
DOI: 0.55/auom-205-0020 An. Şt. Univ. Ovidius Constanţa Vol. 23(),205, 29 30 On neighborhoods of functions associated with conic domains Nihat Yağmur Abstract Let k ST [A, B], k 0, B < A be the class of
More informationVarious Proofs for the Decrease Monotonicity of the Schatten s Power Norm, Various Families of R n Norms and Some Open Problems
Int. J. Oen Problems Comt. Math., Vol. 3, No. 2, June 2010 ISSN 1998-6262; Coyright c ICSRS Publication, 2010 www.i-csrs.org Various Proofs for the Decrease Monotonicity of the Schatten s Power Norm, Various
More informationHEAT AND LAPLACE TYPE EQUATIONS WITH COMPLEX SPATIAL VARIABLES IN WEIGHTED BERGMAN SPACES
Electronic Journal of ifferential Equations, Vol. 207 (207), No. 236,. 8. ISSN: 072-669. URL: htt://ejde.math.txstate.edu or htt://ejde.math.unt.edu HEAT AN LAPLACE TYPE EQUATIONS WITH COMPLEX SPATIAL
More informationQuasi-Convex Functions with Respect to Symmetric Conjugate Points
International Journal of Algebra, Vol. 6, 2012, no. 3, 117-122 Quasi-Convex Functions with Respect to Symmetric Conjugate Points 1 Chew Lai Wah, 2 Aini Janteng and 3 Suzeini Abdul Halim 1,2 School of Science
More informationOn the improvement of Mocanu s conditions
Nunokawa et al. Journal of Inequalities Applications 13, 13:46 http://www.journalofinequalitiesapplications.com/content/13/1/46 R E S E A R C H Open Access On the improvement of Mocanu s conditions M Nunokawa
More informationSOME RESULTS OF p VALENT FUNCTIONS DEFINED BY INTEGRAL OPERATORS. Gulsah Saltik Ayhanoz and Ekrem Kadioglu
Acta Universitatis Aulensis ISSN: 1582-5329 No. 32/2012. 69-85 SOME ESULTS OF VALENT FUNCTIONS EFINE BY INTEAL OPEATOS ulsah Saltik Ayhanoz and Ekre Kadioglu Abstract. In this aer, we derive soe roerties
More informationThe Relationships Between p valent Functions and Univalent Functions
DOI:.55/auom-25-5 An. Şt. Univ. Ovidius Constanţa Vol. 23(),25, 65 72 The Relationships Between p valent Functions and Univalent Functions Murat ÇAĞLAR Abstract In this paper, we obtain some sufficient
More informationFekete-Szegö Problem for Certain Subclass of Analytic Univalent Function using Quasi-Subordination
Mathematica Aeterna, Vol. 3, 203, no. 3, 93-99 Fekete-Szegö Problem for Certain Subclass of Analytic Univalent Function using Quasi-Subordination B. Srutha Keerthi Department of Applied Mathematics Sri
More informationDIFFERENTIAL SUBORDINATION ASSOCIATED WITH NEW GENERALIZED DERIVATIVE OPERATOR
ROMAI J., v.12, no.1(2016), 77 89 DIFFERENTIAL SUBORDINATION ASSOCIATED WITH NEW GENERALIZED DERIVATIVE OPERATOR Anessa Oshah, Maslina Darus School of Mathematical Sciences, Faculty of Science and Technology,
More informationOn sandwich theorems for p-valent functions involving a new generalized differential operator
Stud. Univ. Babeş-Bolyai Math. 60(015), No. 3, 395 40 On sandwich theorems for p-valent functions involving a new generalized differential operator T. Al-Hawary, B.A. Frasin and M. Darus Abstract. A new
More informationOn second-order differential subordinations for a class of analytic functions defined by convolution
Available online at www.isr-publications.co/jnsa J. Nonlinear Sci. Appl., 1 217), 954 963 Research Article Journal Hoepage: www.tjnsa.co - www.isr-publications.co/jnsa On second-order differential subordinations
More informationSubclasses of Analytic Functions. Involving the Hurwitz-Lerch Zeta Function
International Mathematical Forum, Vol. 6, 211, no. 52, 2573-2586 Suclasses of Analytic Functions Involving the Hurwitz-Lerch Zeta Function Shigeyoshi Owa Department of Mathematics Kinki University Higashi-Osaka,
More informationa n z n, z U.. (1) f(z) = z + n=2 n=2 a nz n and g(z) = z + (a 1n...a mn )z n,, z U. n=2 a(a + 1)b(b + 1) z 2 + c(c + 1) 2! +...
ISSN 1749-3889 (print), 1749-3897 (online) International Journal of Nonlinear Science Vol.13(2012) No.2,pp.153-157 Integral Operator Defined by Convolution Product of Hypergeometric Functions Maslina Darus,
More informationSUBCLASSES OF P-VALENT STARLIKE FUNCTIONS DEFINED BY USING CERTAIN FRACTIONAL DERIVATIVE OPERATOR
Sutra: International Journal of Mathematical Science Education Technomathematics Research Foundation Vol. 4 No. 1, pp. 17-32, 2011 SUBCLASSES OF P-VALENT STARLIKE FUNCTIONS DEFINED BY USING CERTAIN FRACTIONAL
More information