ON CO-ORDINATED OSTROWSKI AND HADAMARD S TYPE INEQUALITIES FOR CONVEX FUNCTIONS II
|
|
- Kelley Barker
- 5 years ago
- Views:
Transcription
1 TJMM 9 (7), No., 35-4 ON CO-ORDINATED OSTROWSKI AND HADAMARD S TYPE INEQUALITIES FOR CONVEX FUNCTIONS II MUHAMMAD MUDDASSAR, NASIR SIDDIQUI, AND MUHAMMAD IQBAL Abstrt. In this rtile, we estblish vrious ineulities or some dierentible mppings tht re linked with the illustrious Hermite-Hdmrd nd Ostrowski integrl ineulity or onvex untions o severl-vribles on the o-ordintes.the generlized integrl ineulities ontribute some better estimtes thn some lredy presented.. Introdution In 938, A. Ostrowski proved shrp estimte o dierentible untion, whose irst derivtive is bounded by its integrl men s ollows: Theorem. [ Let : [, b R be dierentible untion on (, b) with bounded derivtive, tht is, <, then (x) [ ( ) (t)dt b x b 4 (b ) (b ), () or ll x [, b. The onstnt 4 is the best possible one. Ineulity () hs lot o pplitions in dierent ields o mthemtis suh s probbility nd numeril nlysis et. Due to tht reson () mke the use o ttention mong mthemtiins nd reserhers. Ineulity () ws improved, generlized nd extended in dierent diretions by using dierent tehniues [, 3, 5, 7. Drgomir [6 deined onvex untion on the o-ordintes s ollows: Deinition. Let us onsider the bi-dimensionl intervl = [, b [, d in R with < b, < d. A untion : [, b R, y (u) = (u, y) nd x : [, d R, x (v) = (x, v) re onvex whose deined or ll y [, d nd x [, b. Rell tht the untion : R is onvex on i (λx ( λ)z, λy ( λ)w) λ(x, y) ( λ)(z, w), holds or ll (x, y), (z, w) nd λ [,. Clerly, every onvex (onve) untion : R is onvex (onve) on the oordintes but onverse my not be true [6. By using this deinition mny reserhers ormulted Ostrowski type ineulities nd in prtiulr gve some shrp estimtes or the let nd right Hdmrd ineulity nd some relted results [, 4, 6, 8, 9, 3. The min im o this pper is to estblish some new Ostrowski type ineulities or o-ordinted onvex untions nd s n pplitions we hve derived let Hdmrd type Mthemtis Subjet Clssiition. Primry 6B5, 6D, 6D5; Seondry 6A48, 6A5, 5A4. Key words nd phrses. o-ordinted onvex untion; Ostrowski ineulity; Hermite- Hdmrd ineulity. 35
2 36 M. MUDDASSAR, N. SIDDIQUI, AND M. IQBAL ineulities. Among those some re shrper thn the exiting one s nd some generlized the exiting one s. This pper is orgnized in the ollowing wy. Ater this Introdution in Setion, we ormulted our min results nd some relted pplitions.. Min Results Lemm. Let : R R be prtil dierentible untion on := [, b [, d with < b nd < d. I L( ), then where, (x, y) A = b I µ,ν = (x µ) (y ν) b (u, y)du d (u, v)dudv A = d (t )(s ) (x, v)dv, I µ,ν, (tµ ( t)x, sν ( s)y)dtds with I µ,ν is positive when (µ, ν) = (, ) nd (b, d) otherwise negtive. Proo. Consider I, = (x ) (y ) (t )(s ) (t ( t)x, s ( s)y)dtds = (x ) (y ) ( ) (s ) (t ) (t ( t)x, s ( s)y)dt ds [ (x )(y ) = ( s) (x, s ( s)y)ds s (t ( t)x, s ( s)y)dsdt = Similrly [ (x )(y ) (x, y) I,d = (x ) (y d) = (x )(y d) [ (x, y) ( s) s (x, s ( s)y)ds (t ( t)x, y)dt (t ( t)x, s ( s)y)dsdt. (t )(s ) (t ( t)x, sd ( s)y)dtds (x, sd ( s)y)ds (t ( t)x, y)dt (t ( t)x, sd ( s)y)dsdt,
3 OSTROWSKI AND HADAMARD S TYPE INEQUALITIES ON CO-ORDINATES 37 I b, = (x b) (y ) = nd (x b)(y ) I b,d = (x b) (y d) = (x b)(y d) [ (x, y) [ (x, y) whih ompletes the proo. (t )(s ) (tb ( t)x, s ( s)y)dtds (x, s ( s)y)ds (tb ( t)x, y)dt (tb ( t)x, s ( s)y)dsdt, (t )(s ) (tb ( t)x, sd ( s)y)dtds (x, sd ( s)y)ds (tb ( t)x, y)dt (tb ( t)x, sd ( s)y)dsdt, Theorem. Let : R R be prtil dierentible untion on := [, b [, d with < b nd < d. I is onvex untion on the o-ordintes on, then (x, y) (u, v)dudv A (x µ) (y ν) 36 [ (µ, ν) (µ, y) (x, ν) 4 (x, y) Proo. By lemm, we hve (x, y) (u, v)dudv A I µ,ν () I µ,ν (x µ) (y ν) Sine : R is oordinted onvex on dtds I µ,ν (x µ) (y ν) { ( s)( t) t (µ, sν ( s)y) ( t) } (x, sν ( s)y) dtds (x µ) (y ν) { ( s)( t) st (µ, ν) ( s)t (µ, y) ( t)s (x, ν) } (x, y) dtds, whih ompletes the proo.
4 38 M. MUDDASSAR, N. SIDDIQUI, AND M. IQBAL Corollry. By setting x = b nd y = d ( ) b, d b (b )(d ) 36 6 (b )(d ) 64 in () we hve d (u, v)dudv A { (µ, ν) ( µ, d ) ( ) b, ν 4 ( b, d )} (µ, ν) (3) Remrk. It my be noted tht (3) gives better pproximtion to [9, Theorem. Theorem 3. Let : R R be prtil dierentible untion on := [, b [, d with < b nd < d. I, > with p =, is onvex untion on the oordintes on, then (x, y) (u, v)dudv A / (x µ) (y ν) (p ) /p ( (µ, ν) (µ, y) Proo. By lemm, we hve (x, y) I µ,ν (x µ) (y ν) By Höder s ineulity I µ,ν (x µ) (y ν) ( (x, ν) (u, v)dudv A / (x, y) ) (4) I µ,ν dtds ( t) p ( s) p dsdt) /p ( ) / dtds By oordinted onvexity o on, we hve (x µ) (y ν) ( { I µ,ν st (p ) /p (µ, ν) ( s)t (µ, y) ( t)s (x, ν) } / (x, y) dtds), whih ompletes the proo.
5 OSTROWSKI AND HADAMARD S TYPE INEQUALITIES ON CO-ORDINATES 39 Remrk. By setting (t, s) M or (t, s) [, b [, d, Theorem 3 redues to [, Theorem 4. The ollowing theorem gives tighter estimte thn tht o previous theorem 3. Theorem 4. Let : R R be prtil dierentible untion on := [, b [, d with < b nd < d. I,, is onvex untion on the o-ordintes on, then (x, y) (u, v)dudv A 3 / (x µ) (y ν) 4 ( (µ, ν) (µ, y) Proo. By lemm, we hve (x, y) I µ,ν (x µ) (y ν) By Höder s ineulity: (x, ν) (u, v)dudv A 4 / (x, y) ) (5) I µ,ν dtds I µ,ν (x µ) (y ν) ( /p dsdt) ( By oordinted onvexity o on, we hve ) / dtds I µ,ν (x µ) (y ν) ( { st /p (µ, ν) ( s)t (µ, y) ( t)s (x, ν) } / (x, y) dtds), whih omplete the proo. Remrk 3. By setting (t, s) M or (t, s) [, b [, d, Theorem 4 redues to [, Theorem 3. Theorem 5. Let : R R be prtil dierentible untion on := [, b [, d with < b nd < d. I, > with /p / = is onve untion on the
6 4 M. MUDDASSAR, N. SIDDIQUI, AND M. IQBAL o-ordintes on, then (x, y) (x µ) (y ν) (p ) /p Proo. By lemm, we hve (x, y) I µ,ν (x µ) (y ν) By Höder s ineulity: I µ,ν (x µ) (y ν) ( (u, v)dudv A ( µ x, ν y ) (6) (u, v)dudv A I µ,ν dtds ( t) p ( s) p dsdt) /p ( By oordinted onvity o on, we hve dtds [ ( tµ ( t)x, ν y ) dt ( ) µ x, sν ( s)y ( µ x, ν y ), ds ) / dtds whih ompletes the proo. Theorem 6. Let : R R be prtil dierentible mpping on := [, b [, d with < b nd < d. I,, is onve untion on the o-ordintes on, then (x, y) (u, v)dudv A (x µ) (y ν) ( µ x 4, ν y ) (7) 3 3
7 OSTROWSKI AND HADAMARD S TYPE INEQUALITIES ON CO-ORDINATES 4 Proo. By the onvity o on the o-ordintes on nd power-men ineulity, the ollowing ineulity holds: (tµ ( t)x, v) t (µ, v) ( t) (x, v) ( t (µ, v) ( t) ) (x, v) or ll µ, x [, b, t [, nd ixed v [, d (tµ ( t)x, v) t (µ, v) ( t) (x, v). Similrly (u, sν ( s)y) s (u, ν) ( s) (u, y), or ll ν, y [, d, s [, nd ixed u [, b, showing tht is onve on o-ordintes on. Now by lemm (x, y) (u, v)dudv A I µ,ν. I µ,ν (x µ) (y ν) dtds. By oordinted onvity o on, nd Jensen s integrl ineulity, we hve dtds [ = ( t) ( s) ds ds [ ( ( t) ( s)ds) ( ) ( s)(sν ( s)y)ds tµ ( t)x, ( s)ds dt = ( t) ( tµ ( t)x, ν y ) dt 3 ( ( t)dt) ( ) ( t)(tµ ( t)x)dt, ν y ( t)dt 3 = ( µ x 4, ν y ) dt, 3 3 whih ompletes the proo. Remrk 4. By setting x = b, y = d, Theorem 6 redues to [9, Theorem 5. Authors ontributions: All uthors ontributed eully in this rtile. They red nd pproved the inl mnusript. Aknowledgments: This reserh pper is mde possible through the help nd support rom HEC, Pkistn nd Univ. o the Engg. & Teh. Txil, Pkistn. We grteully
8 4 M. MUDDASSAR, N. SIDDIQUI, AND M. IQBAL knowledge the time nd expertise devoted to reviewing ppers by the dvisory editors, the members o the editoril bord, nd the reerees. Finlly, We would like to express our tribute to Pro. Dr. Muhmmd Ibl Bhtti (Chirmn, Dept. o Mth., UET, Txil), Our dotorl Supervisor, who died young in his work. As tlented nd outstnding young proessor, you sriied your lie to the ountry when your reer ws thriving. We will never orget how muh you red bout our study nd dily lie. We will miss you orever! Reerenes [ Alomri, M. nd Drus, M., Some Ostrowski type ineulities or onvex untions with pplitions, RGMIA 3 (). Artile No. 3. [ Alomri, M. nd Drus, M., The Hdmrd s ineulity or s-onvex untions o -vribles, Int. Jour. Mth. Anl. (3), (8), [3 Alomri, M., Drus, M., Drgomir, S.S., Cerone, P., Ostroski type ineulities or untions whose derivtives re s-onvex in seond sense, Appl. Mth. Lett. 3 (), [4 Bkul M.K., nd Pečrić, J., On the Jensen s ineulity or onvex untions on the o-ordintes in retngle rom the plne, Tiwnese Journl o Mthemtis 5 (6), 7 9. [5 Cerone, P., Drgomir, S.S., Roumeliots, J., An ineulity o Ostrowski-Grüss type or twie dierentible mppings nd pplitions in numeril integrtion, Kyungpook Mth. J. 39 (999), [6 Drgomir, S.S., On Hdmrd ineulity or onvex untions on o-ordintes in retngle rom the plne, Tiwnese Journl o Mthemtis, 5 (), [7 Drgomir, S.S., Cerone, P., Roumelities, J., A new generliztion o Ostrowski integrl ineulity or mpping whose derivtives re bounded nd pplitions in numeril integrtion nd or speil mens, Appl. Mth. Lett. 3 (), 9 5. [8 Lti, M.A. nd Alomri, M., Hdmrd-type ineulities or produt two onvex untions on the o-ordintes, Int. Mth. Forum 4 (47), (9), [9 Lti, M.A. nd Drgomir, S.S., On some new ineulities or dierentible o-ordinted onvex untions, Jour. Ine. Appl. :8, doi:.86/9-4x--8. [ Lti, M.A., Hussin, S. nd Drgomir, S.S., New Ostrowski type ineulities o o-ordinted onvex untions, ON-LINE: [ Mitrinović, D.S., Pečrić, J.E. nd Fink, A.M., Ineulities Involving Funtions nd their Integrls nd Derivtives, Kluwer Ademi Publishers, Dortreht, 99. [ Ostrowski, A., Über die Absolutbweihung einer dierentiebren unktin von ihren intergrlmittelwert, Comment. Mth. Helv. (938), 6 7. [3 Özdemir, M.E., Kvurmi, H., Akdemir, A.O. nd Avi, M., Ineulities or onvex nd s-onvex untions on = [, b [, d, Jour. Ine. Appl.,. Deprtment o Mthemtis Govt. College o Siene, Lhore - Pkistn E-mil ddress: mlik.muddssr@gmil.om Deprtment o Mthemtis University o Engineering nd Tehnology, Txil - Pkistn E-mil ddress: nsir.siddiui@uettxil.edu.pk Deprtment o Mthemtis Govt. Islmi College, Civil Lines Lhore- Pkistn E-mil ddress: mibl.bki@gmil.om
On the Co-Ordinated Convex Functions
Appl. Mth. In. Si. 8, No. 3, 085-0 0 085 Applied Mthemtis & Inormtion Sienes An Interntionl Journl http://.doi.org/0.785/mis/08038 On the Co-Ordinted Convex Funtions M. Emin Özdemir, Çetin Yıldız, nd Ahmet
More informationCo-ordinated s-convex Function in the First Sense with Some Hadamard-Type Inequalities
Int. J. Contemp. Mth. Sienes, Vol. 3, 008, no. 3, 557-567 Co-ordinted s-convex Funtion in the First Sense with Some Hdmrd-Type Inequlities Mohmmd Alomri nd Mslin Drus Shool o Mthemtil Sienes Fulty o Siene
More informationSome integral inequalities of the Hermite Hadamard type for log-convex functions on co-ordinates
Avilble online t www.tjns.om J. Nonliner Si. Appl. 9 06), 5900 5908 Reserh Artile Some integrl inequlities o the Hermite Hdmrd type or log-onvex untions on o-ordintes Yu-Mei Bi, Feng Qi b,, College o Mthemtis,
More informationSOME NEW HERMITE-HADAMARD TYPE INEQUALITIES FOR FUNCTIONS WHOSE HIGHER ORDER PARTIAL DERIVATIVES ARE CO-ORDINATED CONVEX
FACTA UNIVERSITATIS (NIŠ) Ser. Mth. Inor. Vol. 7 No 3 (), 3 336 SOME NEW HERMITE-HADAMARD TYPE INEQUALITIES FOR FUNCTIONS WHOSE HIGHER ORDER PARTIAL DERIVATIVES ARE CO-ORDINATED CONVEX Muhd Aer Lti nd
More informationHermite-Hadamard inequality for geometrically quasiconvex functions on co-ordinates
Int. J. Nonliner Anl. Appl. 8 27 No. 47-6 ISSN: 28-6822 eletroni http://dx.doi.org/.2275/ijn.26.483 Hermite-Hdmrd ineulity for geometrilly usionvex funtions on o-ordintes Ali Brni Ftemeh Mlmir Deprtment
More informationInequalities for convex and s-convex functions on Δ =[a, b] [c, d]
Özdemir et l. Journl o Ineulities nd Applitions, : http://www.journloineulitiesndpplitions.om/ontent/// RESEARCH Open Aess Ineulities or onvex nd s-onvex untions on Δ =, b], d] Muhmet Emin Özdemir, Hvv
More informationHadamard-Type Inequalities for s-convex Functions
Interntionl Mthemtil Forum, 3, 008, no. 40, 965-975 Hdmrd-Type Inequlitie or -Convex Funtion Mohmmd Alomri nd Mlin Dru Shool o Mthemtil Siene Fulty o Siene nd Tehnology Univeriti Kebngn Mlyi Bngi 43600
More informationThe Hadamard s inequality for quasi-convex functions via fractional integrals
Annls of the University of Criov, Mthemtics nd Computer Science Series Volume (), 3, Pges 67 73 ISSN: 5-563 The Hdmrd s ineulity for usi-convex functions vi frctionl integrls M E Özdemir nd Çetin Yildiz
More informationNEW INEQUALITIES OF OSTROWSKI TYPE FOR CO-ORDINATED s-convex FUNCTIONS VIA FRACTIONAL INTEGRALS
Journl of Frtionl Clulus nd Applitions, Vol. 4() Jn. 3, pp. -36. ISSN: 9-5858. http://www.fj.webs.om/ NEW INEQUALITIES OF OSTROWSKI TYPE FOR CO-ORDINATED s-convex FUNCTIONS VIA FRACTIONAL INTEGRALS M.
More informationNew general integral inequalities for quasiconvex functions
NTMSCI 6, No 1, 1-7 18 1 New Trends in Mthemticl Sciences http://dxdoiorg/185/ntmsci1739 New generl integrl ineulities for usiconvex functions Cetin Yildiz Atturk University, K K Eduction Fculty, Deprtment
More informationDIFFERENCE BETWEEN TWO RIEMANN-STIELTJES INTEGRAL MEANS
Krgujev Journl of Mthemtis Volume 38() (204), Pges 35 49. DIFFERENCE BETWEEN TWO RIEMANN-STIELTJES INTEGRAL MEANS MOHAMMAD W. ALOMARI Abstrt. In this pper, severl bouns for the ifferene between two Riemn-
More informationHadamard-Type Inequalities for s Convex Functions I
Punjb University Journl of Mthemtics ISSN 6-56) Vol. ). 5-6 Hdmrd-Tye Ineulities for s Convex Functions I S. Hussin Dertment of Mthemtics Institute Of Sce Technology, Ner Rwt Toll Plz Islmbd Highwy, Islmbd
More informationNEW INEQUALITIES OF SIMPSON S TYPE FOR s CONVEX FUNCTIONS WITH APPLICATIONS. := f (4) (x) <. The following inequality. 2 b a
NEW INEQUALITIES OF SIMPSON S TYPE FOR s CONVEX FUNCTIONS WITH APPLICATIONS MOHAMMAD ALOMARI A MASLINA DARUS A AND SEVER S DRAGOMIR B Abstrct In terms of the first derivtive some ineulities of Simpson
More informationBulletin of the. Iranian Mathematical Society
ISSN: 07-060X Print ISSN: 735-855 Online Bulletin of the Irnin Mthemticl Society Vol 3 07, No, pp 09 5 Title: Some extended Simpson-type ineulities nd pplictions Authors: K-C Hsu, S-R Hwng nd K-L Tseng
More informationON THE INEQUALITY OF THE DIFFERENCE OF TWO INTEGRAL MEANS AND APPLICATIONS FOR PDFs
ON THE INEQUALITY OF THE DIFFERENCE OF TWO INTEGRAL MEANS AND APPLICATIONS FOR PDFs A.I. KECHRINIOTIS AND N.D. ASSIMAKIS Deprtment of Eletronis Tehnologil Edutionl Institute of Lmi, Greee EMil: {kehrin,
More informationIntegral inequalities for n times differentiable mappings
JACM 3, No, 36-45 8 36 Journl of Abstrct nd Computtionl Mthemtics http://wwwntmscicom/jcm Integrl ineulities for n times differentible mppings Cetin Yildiz, Sever S Drgomir Attur University, K K Eduction
More informationarxiv: v1 [math.ca] 28 Jan 2013
ON NEW APPROACH HADAMARD-TYPE INEQUALITIES FOR s-geometrically CONVEX FUNCTIONS rxiv:3.9v [mth.ca 8 Jn 3 MEVLÜT TUNÇ AND İBRAHİM KARABAYIR Astrct. In this pper we chieve some new Hdmrd type ineulities
More informationHermite-Hadamard type inequalities for harmonically convex functions
Hcettepe Journl o Mthemtics nd Sttistics Volume 43 6 4 935 94 Hermite-Hdmrd type ineulities or hrmoniclly convex unctions İmdt İşcn Abstrct The uthor introduces the concept o hrmoniclly convex unctions
More informationNew Integral Inequalities of the Type of Hermite-Hadamard Through Quasi Convexity
Punjb University Journl of Mthemtics (ISSN 116-56) Vol. 45 (13) pp. 33-38 New Integrl Inequlities of the Type of Hermite-Hdmrd Through Qusi Convexity S. Hussin Deprtment of Mthemtics, College of Science,
More informationThe Hadamard s Inequality for s-convex Function
Int. Journl o Mth. Anlysis, Vol., 008, no. 3, 639-646 The Hdmrd s Inequlity or s-conve Function M. Alomri nd M. Drus School o Mthemticl Sciences Fculty o Science nd Technology Universiti Kebngsn Mlysi
More informationNEW HERMITE HADAMARD INEQUALITIES VIA FRACTIONAL INTEGRALS, WHOSE ABSOLUTE VALUES OF SECOND DERIVATIVES IS P CONVEX
Journl of Mthemticl Ineulities Volume 1, Number 3 18, 655 664 doi:1.7153/jmi-18-1-5 NEW HERMITE HADAMARD INEQUALITIES VIA FRACTIONAL INTEGRALS, WHOSE ABSOLUTE VALUES OF SECOND DERIVATIVES IS P CONVEX SHAHID
More informationSome estimates on the Hermite-Hadamard inequality through quasi-convex functions
Annls of University of Criov, Mth. Comp. Sci. Ser. Volume 3, 7, Pges 8 87 ISSN: 13-693 Some estimtes on the Hermite-Hdmrd inequlity through qusi-convex functions Dniel Alexndru Ion Abstrct. In this pper
More informationf (a) + f (b) f (λx + (1 λ)y) max {f (x),f (y)}, x, y [a, b]. (1.1)
TAMKANG JOURNAL OF MATHEMATICS Volume 41, Number 4, 353-359, Winter 1 NEW INEQUALITIES OF HERMITE-HADAMARD TYPE FOR FUNCTIONS WHOSE SECOND DERIVATIVES ABSOLUTE VALUES ARE QUASI-CONVEX M. ALOMARI, M. DARUS
More informationON SOME NEW INEQUALITIES OF HADAMARD TYPE INVOLVING h-convex FUNCTIONS. 1. Introduction. f(a) + f(b) f(x)dx b a. 2 a
Act Mth. Univ. Comenine Vol. LXXIX, (00, pp. 65 7 65 ON SOME NEW INEQUALITIES OF HADAMARD TYPE INVOLVING h-convex FUNCTIONS M. Z. SARIKAYA, E. SET nd M. E. ÖZDEMIR Abstrct. In this pper, we estblish some
More informationSOME INEQUALITIES FOR THE DISPERSION OF A RANDOM VARIABLE WHOSE PDF IS DEFINED ON A FINITE INTERVAL
SOME INEQUALITIES FOR THE DISPERSION OF A RANDOM VARIABLE WHOSE PDF IS DEFINED ON A FINITE INTERVAL NS BARNETT P CERONE SS DRAGOMIR AND J ROUMELIOTIS Abstrct Some ineulities for the dispersion of rndom
More informationSOME NEW HERMITE-HADAMARD TYPE INEQUALITIES FOR FUNCTIONS WHOSE HIGHER ORDER PARTIAL DERIVATIVES ARE CO-ORDINATED s-convex
Krgujev Journl of Mthetis Volue 38 4, Pges 5 46 SOME NEW HERMITE-HADAMARD TYPE INEQUALITIES FOR FUNCTIONS WHOSE HIGHER ORDER PARTIAL DERIVATIVES ARE CO-ORDINATED s-convex MUHAMMAD AMER LATIF Abstrt In
More informationSome inequalities of Hermite-Hadamard type for n times differentiable (ρ, m) geometrically convex functions
Avilble online t www.tjns.com J. Nonliner Sci. Appl. 8 5, 7 Reserch Article Some ineulities of Hermite-Hdmrd type for n times differentible ρ, m geometriclly convex functions Fiz Zfr,, Humir Klsoom, Nwb
More informationOn some refinements of companions of Fejér s inequality via superquadratic functions
Proyecciones Journl o Mthemtics Vol. 3, N o, pp. 39-33, December. Universidd Ctólic del Norte Antogst - Chile On some reinements o compnions o Fejér s inequlity vi superqudrtic unctions Muhmmd Amer Lti
More informationKeywords : Generalized Ostrowski s inequality, generalized midpoint inequality, Taylor s formula.
Generliztions of the Ostrowski s inequlity K. S. Anstsiou Aristides I. Kechriniotis B. A. Kotsos Technologicl Eductionl Institute T.E.I.) of Lmi 3rd Km. O.N.R. Lmi-Athens Lmi 3500 Greece Abstrct Using
More informationParametrized inequality of Hermite Hadamard type for functions whose third derivative absolute values are quasi convex
Wu et l. SpringerPlus (5) 4:83 DOI.8/s44-5-33-z RESEARCH Prmetrized inequlity of Hermite Hdmrd type for functions whose third derivtive bsolute vlues re qusi convex Shn He Wu, Bnyt Sroysng, Jin Shn Xie
More informationJournal of Inequalities in Pure and Applied Mathematics
Journl of Inequlities in Pure nd Applied Mthemtics http://jipmvueduu/ Volume, Issue, Article, 00 SOME INEQUALITIES FOR THE DISPERSION OF A RANDOM VARIABLE WHOSE PDF IS DEFINED ON A FINITE INTERVAL NS BARNETT,
More informationOstrowski Grüss Čebyšev type inequalities for functions whose modulus of second derivatives are convex 1
Generl Mthemtics Vol. 6, No. (28), 7 97 Ostrowski Grüss Čebyšev type inequlities for functions whose modulus of second derivtives re convex Nzir Ahmd Mir, Arif Rfiq nd Muhmmd Rizwn Abstrct In this pper,
More informationOn Hermite-Hadamard type integral inequalities for functions whose second derivative are nonconvex
Mly J Mt 34 93 3 On Hermite-Hdmrd tye integrl ineulities for functions whose second derivtive re nonconvex Mehmet Zeki SARIKAYA, Hkn Bozkurt nd Mehmet Eyü KİRİŞ b Dertment of Mthemtics, Fculty of Science
More informationHermite-Hadamard Type Inequalities for the Functions whose Second Derivatives in Absolute Value are Convex and Concave
Applied Mthemticl Sciences Vol. 9 05 no. 5-36 HIKARI Ltd www.m-hikri.com http://d.doi.org/0.988/ms.05.9 Hermite-Hdmrd Type Ineulities for the Functions whose Second Derivtives in Absolute Vlue re Conve
More informationOn some inequalities for s-convex functions and applications
Özdemir et l Journl of Ineulities nd Alictions 3, 3:333 htt://wwwjournlofineulitiesndlictionscom/content/3//333 R E S E A R C H Oen Access On some ineulities for s-convex functions nd lictions Muhmet Emin
More informationResearch Article On The Hadamard s Inequality for Log-Convex Functions on the Coordinates
Hindwi Publishing Corportion Journl of Inequlities nd Applictions Volume 29, Article ID 28347, 3 pges doi:.55/29/28347 Reserch Article On The Hdmrd s Inequlity for Log-Convex Functions on the Coordintes
More informationA Companion of Ostrowski Type Integral Inequality Using a 5-Step Kernel with Some Applications
Filomt 30:3 06, 360 36 DOI 0.9/FIL6360Q Pulished y Fculty of Sciences nd Mthemtics, University of Niš, Seri Aville t: http://www.pmf.ni.c.rs/filomt A Compnion of Ostrowski Type Integrl Inequlity Using
More informationJournal of Inequalities in Pure and Applied Mathematics
Journl of Inequlities in Pure nd Applied Mthemtics GENERALIZATIONS OF THE TRAPEZOID INEQUALITIES BASED ON A NEW MEAN VALUE THEOREM FOR THE REMAINDER IN TAYLOR S FORMULA volume 7, issue 3, rticle 90, 006.
More informationOn new Hermite-Hadamard-Fejer type inequalities for p-convex functions via fractional integrals
CMMA, No., -5 7 Communiction in Mthemticl Modeling nd Applictions http://ntmsci.com/cmm On new Hermite-Hdmrd-Fejer type ineulities or p-convex unctions vi rctionl integrls Mehmet Kunt nd Imdt Iscn Deprtment
More informationS. S. Dragomir. 2, we have the inequality. b a
Bull Koren Mth Soc 005 No pp 3 30 SOME COMPANIONS OF OSTROWSKI S INEQUALITY FOR ABSOLUTELY CONTINUOUS FUNCTIONS AND APPLICATIONS S S Drgomir Abstrct Compnions of Ostrowski s integrl ineulity for bsolutely
More informationSome new integral inequalities for n-times differentiable convex and concave functions
Avilble online t wwwisr-ublictionscom/jns J Nonliner Sci Al, 10 017, 6141 6148 Reserch Article Journl Homege: wwwtjnscom - wwwisr-ublictionscom/jns Some new integrl ineulities for n-times differentible
More informationImprovement of Ostrowski Integral Type Inequalities with Application
Filomt 30:6 06), 56 DOI 098/FIL606Q Published by Fculty of Sciences nd Mthemtics, University of Niš, Serbi Avilble t: http://wwwpmfnicrs/filomt Improvement of Ostrowski Integrl Type Ineulities with Appliction
More informationAN INEQUALITY OF OSTROWSKI TYPE AND ITS APPLICATIONS FOR SIMPSON S RULE AND SPECIAL MEANS. I. Fedotov and S. S. Dragomir
RGMIA Reserch Report Collection, Vol., No., 999 http://sci.vu.edu.u/ rgmi AN INEQUALITY OF OSTROWSKI TYPE AND ITS APPLICATIONS FOR SIMPSON S RULE AND SPECIAL MEANS I. Fedotov nd S. S. Drgomir Astrct. An
More informationGeneralized Hermite-Hadamard Type Inequalities for p -Quasi- Convex Functions
Ordu Üniv. Bil. Tek. Derg. Cilt:6 Syı: 683-93/Ordu Univ. J. Sci. Tech. Vol:6 No:683-93 -QUASİ-KONVEKS FONKSİYONLAR İÇİN GENELLEŞTİRİLMİŞ HERMİTE-HADAMARD TİPLİ EŞİTSİZLİKLER Özet İm İŞCAN* Giresun Üniversitesi
More informationAN INTEGRAL INEQUALITY FOR CONVEX FUNCTIONS AND APPLICATIONS IN NUMERICAL INTEGRATION
Applied Mthemtics E-Notes, 5(005), 53-60 c ISSN 1607-510 Avilble free t mirror sites of http://www.mth.nthu.edu.tw/ men/ AN INTEGRAL INEQUALITY FOR CONVEX FUNCTIONS AND APPLICATIONS IN NUMERICAL INTEGRATION
More informationJournal of Inequalities in Pure and Applied Mathematics
Journl of Inequlities in Pure nd Applied Mthemtics SOME INEQUALITIES FOR THE DISPERSION OF A RANDOM VARI- ABLE WHOSE PDF IS DEFINED ON A FINITE INTERVAL NEIL S. BARNETT, PIETRO CERONE, SEVER S. DRAGOMIR
More informationON PERTURBED TRAPEZOIDAL AND MIDPOINT RULES. f (t) dt
ON PERTURBED TRAPEZOIDAL AND MIDPOINT RULES P. CERONE Abstrct. Explicit bounds re obtined for the perturbed or corrected trpezoidl nd midpoint rules in terms of the Lebesque norms of the second derivtive
More informationON AN INTEGRATION-BY-PARTS FORMULA FOR MEASURES
Volume 8 (2007), Issue 4, Article 93, 13 pp. ON AN INTEGRATION-BY-PARTS FORMULA FOR MEASURES A. ČIVLJAK, LJ. DEDIĆ, AND M. MATIĆ AMERICAN COLLEGE OF MANAGEMENT AND TECHNOLOGY ROCHESTER INSTITUTE OF TECHNOLOGY
More informationA Generalized Inequality of Ostrowski Type for Twice Differentiable Bounded Mappings and Applications
Applied Mthemticl Sciences, Vol. 8, 04, no. 38, 889-90 HIKARI Ltd, www.m-hikri.com http://dx.doi.org/0.988/ms.04.4 A Generlized Inequlity of Ostrowski Type for Twice Differentile Bounded Mppings nd Applictions
More informationON COMPANION OF OSTROWSKI INEQUALITY FOR MAPPINGS WHOSE FIRST DERIVATIVES ABSOLUTE VALUE ARE CONVEX WITH APPLICATIONS
Miskolc Mthemticl Notes HU ISSN 787-5 Vol. 3 (), No., pp. 33 8 ON OMPANION OF OSTROWSKI INEQUALITY FOR MAPPINGS WHOSE FIRST DERIVATIVES ABSOLUTE VALUE ARE ONVEX WITH APPLIATIONS MOHAMMAD W. ALOMARI, M.
More informationS. S. Dragomir. 1. Introduction. In [1], Guessab and Schmeisser have proved among others, the following companion of Ostrowski s inequality:
FACTA UNIVERSITATIS NIŠ) Ser Mth Inform 9 00) 6 SOME COMPANIONS OF OSTROWSKI S INEQUALITY FOR ABSOLUTELY CONTINUOUS FUNCTIONS AND APPLICATIONS S S Drgomir Dedicted to Prof G Mstroinni for his 65th birthdy
More informationSOME INTEGRAL INEQUALITIES OF GRÜSS TYPE
RGMIA Reserch Report Collection, Vol., No., 998 http://sci.vut.edu.u/ rgmi SOME INTEGRAL INEQUALITIES OF GRÜSS TYPE S.S. DRAGOMIR Astrct. Some clssicl nd new integrl inequlities of Grüss type re presented.
More informationTRAPEZOIDAL TYPE INEQUALITIES FOR n TIME DIFFERENTIABLE FUNCTIONS
TRAPEZOIDAL TYPE INEQUALITIES FOR n TIME DIFFERENTIABLE FUNCTIONS S.S. DRAGOMIR AND A. SOFO Abstrct. In this pper by utilising result given by Fink we obtin some new results relting to the trpezoidl inequlity
More informationINEQUALITIES OF HERMITE-HADAMARD S TYPE FOR FUNCTIONS WHOSE DERIVATIVES ABSOLUTE VALUES ARE QUASI-CONVEX
INEQUALITIES OF HERMITE-HADAMARD S TYPE FOR FUNCTIONS WHOSE DERIVATIVES ABSOLUTE VALUES ARE QUASI-CONVEX M. ALOMARI A, M. DARUS A, AND S.S. DRAGOMIR B Astrct. In this er, some ineulities of Hermite-Hdmrd
More informationGENERALIZED OSTROWSKI TYPE INEQUALITIES FOR FUNCTIONS WHOSE LOCAL FRACTIONAL DERIVATIVES ARE GENERALIZED s-convex IN THE SECOND SENSE
Journl of Alied Mthemtics nd Comuttionl Mechnics 6, 5(4), - wwwmcmczl -ISSN 99-9965 DOI: 75/jmcm64 e-issn 353-588 GENERALIZED OSTROWSKI TYPE INEQUALITIES FOR FUNCTIONS WHOSE LOCAL FRACTIONAL DERIVATIVES
More informationSome Hermite-Hadamard type inequalities for functions whose exponentials are convex
Stud. Univ. Beş-Bolyi Mth. 6005, No. 4, 57 534 Some Hermite-Hdmrd type inequlities for functions whose exponentils re convex Silvestru Sever Drgomir nd In Gomm Astrct. Some inequlities of Hermite-Hdmrd
More informationThe study of dual integral equations with generalized Legendre functions
J. Mth. Anl. Appl. 34 (5) 75 733 www.elsevier.om/lote/jm The study of dul integrl equtions with generlized Legendre funtions B.M. Singh, J. Rokne,R.S.Dhliwl Deprtment of Mthemtis, The University of Clgry,
More informationResearch Article On Hermite-Hadamard Type Inequalities for Functions Whose Second Derivatives Absolute Values Are s-convex
ISRN Applied Mthemtics, Article ID 8958, 4 pges http://dx.doi.org/.55/4/8958 Reserch Article On Hermite-Hdmrd Type Inequlities for Functions Whose Second Derivtives Absolute Vlues Are s-convex Feixing
More informationAn inequality related to η-convex functions (II)
Int. J. Nonliner Anl. Appl. 6 (15) No., 7-33 ISSN: 8-68 (electronic) http://d.doi.org/1.75/ijn.15.51 An inequlity relted to η-conve functions (II) M. Eshghi Gordji, S. S. Drgomir b, M. Rostmin Delvr, Deprtment
More informationImprovements of some Integral Inequalities of H. Gauchman involving Taylor s Remainder
Divulgciones Mtemátics Vol. 11 No. 2(2003), pp. 115 120 Improvements of some Integrl Inequlities of H. Guchmn involving Tylor s Reminder Mejor de lguns Desigulddes Integrles de H. Guchmn que involucrn
More informationSOME INTEGRAL INEQUALITIES FOR HARMONICALLY CONVEX STOCHASTIC PROCESSES ON THE CO-ORDINATES
Avne Mth Moels & Applitions Vol3 No 8 pp63-75 SOME INTEGRAL INEQUALITIES FOR HARMONICALLY CONVE STOCHASTIC PROCESSES ON THE CO-ORDINATES Nurgül Okur * Imt Işn Yusuf Ust 3 3 Giresun University Deprtment
More informationOn New Inequalities of Hermite-Hadamard-Fejer Type for Harmonically Quasi-Convex Functions Via Fractional Integrals
X th Interntionl Sttistics Dys Conference ISDC 6), Giresun, Turkey On New Ineulities of Hermite-Hdmrd-Fejer Type for Hrmoniclly Qusi-Convex Functions Vi Frctionl Integrls Mehmet Kunt * nd İmdt İşcn Deprtment
More informationA unified generalization of perturbed mid-point and trapezoid inequalities and asymptotic expressions for its error term
An. Ştiinţ. Univ. Al. I. Cuz Işi. Mt. (N.S. Tomul LXIII, 07, f. A unified generliztion of perturbed mid-point nd trpezoid inequlities nd symptotic expressions for its error term Wenjun Liu Received: 7.XI.0
More informationWENJUN LIU AND QUÔ C ANH NGÔ
AN OSTROWSKI-GRÜSS TYPE INEQUALITY ON TIME SCALES WENJUN LIU AND QUÔ C ANH NGÔ Astrct. In this pper we derive new inequlity of Ostrowski-Grüss type on time scles nd thus unify corresponding continuous
More informationNew Integral Inequalities for n-time Differentiable Functions with Applications for pdfs
Applied Mthemticl Sciences, Vol. 2, 2008, no. 8, 353-362 New Integrl Inequlities for n-time Differentible Functions with Applictions for pdfs Aristides I. Kechriniotis Technologicl Eductionl Institute
More informationRevista Colombiana de Matemáticas Volumen 41 (2007), páginas 1 13
Revist Colombin de Mtemátics Volumen 4 7, págins 3 Ostrowski, Grüss, Čebyšev type inequlities for functions whose second derivtives belong to Lp,b nd whose modulus of second derivtives re convex Arif Rfiq
More informationHERMITE-HADAMARD TYPE INEQUALITIES FOR FUNCTIONS WHOSE DERIVATIVES ARE (α, m)-convex
HERMITE-HADAMARD TYPE INEQUALITIES FOR FUNCTIONS WHOSE DERIVATIVES ARE (α -CONVEX İMDAT İŞCAN Dertent of Mthetics Fculty of Science nd Arts Giresun University 8 Giresun Turkey idtiscn@giresunedutr Abstrct:
More informationHyers-Ulam stability of Pielou logistic difference equation
vilble online t wwwisr-publitionsom/jns J Nonliner Si ppl, 0 (207, 35 322 Reserh rtile Journl Homepge: wwwtjnsom - wwwisr-publitionsom/jns Hyers-Ulm stbility of Pielou logisti differene eqution Soon-Mo
More informationGENERALIZATIONS OF WEIGHTED TRAPEZOIDAL INEQUALITY FOR MONOTONIC MAPPINGS AND ITS APPLICATIONS. (b a)3 [f(a) + f(b)] f x (a,b)
GENERALIZATIONS OF WEIGHTED TRAPEZOIDAL INEQUALITY FOR MONOTONIC MAPPINGS AND ITS APPLICATIONS KUEI-LIN TSENG, GOU-SHENG YANG, AND SEVER S. DRAGOMIR Abstrct. In this pper, we estblish some generliztions
More informationAn optimal 3-point quadrature formula of closed type and error bounds
Revist Colombin de Mtemátics Volumen 8), págins 9- An optiml 3-point qudrture formul of closed type nd error bounds Un fórmul de cudrtur óptim de 3 puntos de tipo cerrdo y error de fronter Nend Ujević,
More informationResearch Article On New Inequalities via Riemann-Liouville Fractional Integration
Abstrct nd Applied Anlysis Volume 202, Article ID 428983, 0 pges doi:0.55/202/428983 Reserch Article On New Inequlities vi Riemnn-Liouville Frctionl Integrtion Mehmet Zeki Sriky nd Hsn Ogunmez 2 Deprtment
More informationSome New Inequalities of Simpson s Type for s-convex Functions via Fractional Integrals
Filomt 3:5 (7), 4989 4997 htts://doi.org/.98/fil75989c Published by Fculty o Sciences nd Mthemtics, University o Niš, Serbi Avilble t: htt://www.m.ni.c.rs/ilomt Some New Ineulities o Simson s Tye or s-convex
More informationHermite-Hadamard-Fejér type inequalities for harmonically convex functions via fractional integrals
NTMSCI 4, No. 3, 39-53 6 39 New Trends in Mthemticl Sciences http://d.doi.or/.5/ntmsci.6337 Hermite-Hdmrd-Fejér type ineulities or hrmoniclly conve unctions vi rctionl interls Imdt Iscn, Mehmet Kunt nd
More informationImprovement of Grüss and Ostrowski Type Inequalities
Filomt 9:9 (05), 07 035 DOI 098/FIL50907A Pulished y Fculty of Sciences nd Mthemtics, University of Niš, Seri Aville t: http://wwwpmfnicrs/filomt Improvement of Grüss nd Ostrowski Type Inequlities An Mri
More informationJournal of Inequalities in Pure and Applied Mathematics
Journl of Inequlities in Pure nd Applied Mthemtics MOMENTS INEQUALITIES OF A RANDOM VARIABLE DEFINED OVER A FINITE INTERVAL PRANESH KUMAR Deprtment of Mthemtics & Computer Science University of Northern
More informationON THE WEIGHTED OSTROWSKI INEQUALITY
ON THE WEIGHTED OSTROWSKI INEQUALITY N.S. BARNETT AND S.S. DRAGOMIR School of Computer Science nd Mthemtics Victori University, PO Bo 14428 Melbourne City, VIC 8001, Austrli. EMil: {neil.brnett, sever.drgomir}@vu.edu.u
More informationON NEW INEQUALITIES OF SIMPSON S TYPE FOR FUNCTIONS WHOSE SECOND DERIVATIVES ABSOLUTE VALUES ARE CONVEX
Journl of Applied Mhemics, Sisics nd Informics JAMSI), 9 ), No. ON NEW INEQUALITIES OF SIMPSON S TYPE FOR FUNCTIONS WHOSE SECOND DERIVATIVES ABSOLUTE VALUES ARE CONVEX MEHMET ZEKI SARIKAYA, ERHAN. SET
More informationn-points Inequalities of Hermite-Hadamard Type for h-convex Functions on Linear Spaces
Armenin Journl o Mthemtics Volume 8, Number, 6, 38 57 n-points Inequlities o Hermite-Hdmrd Tpe or h-convex Functions on Liner Spces S. S. Drgomir Victori Universit, Universit o the Witwtersrnd Abstrct.
More informationBounds for the Riemann Stieltjes integral via s-convex integrand or integrator
ACTA ET COMMENTATIONES UNIVERSITATIS TARTUENSIS DE MATHEMATICA Volume 6, Number, 0 Avilble online t www.mth.ut.ee/ct/ Bounds for the Riemnn Stieltjes integrl vi s-convex integrnd or integrtor Mohmmd Wjeeh
More informationMA10207B: ANALYSIS SECOND SEMESTER OUTLINE NOTES
MA10207B: ANALYSIS SECOND SEMESTER OUTLINE NOTES CHARLIE COLLIER UNIVERSITY OF BATH These notes hve been typeset by Chrlie Collier nd re bsed on the leture notes by Adrin Hill nd Thoms Cottrell. These
More information6.1 Definition of the Riemann Integral
6 The Riemnn Integrl 6. Deinition o the Riemnn Integrl Deinition 6.. Given n intervl [, b] with < b, prtition P o [, b] is inite set o points {x, x,..., x n } [, b], lled grid points, suh tht x =, x n
More informationRIEMANN-LIOUVILLE FRACTIONAL SIMPSON S INEQUALITIES THROUGH GENERALIZED (m, h 1, h 2 )-PREINVEXITY
ITALIAN JOURNAL OF PURE AND APPLIED MATHEMATICS N. 38 7 345 37 345 RIEMANN-LIOUVILLE FRACTIONAL SIMPSON S INEQUALITIES THROUGH GENERALIZED m h h -PREINVEXITY Cheng Peng Chng Zhou Tingsong Du Deprtment
More informationMUHAMMAD MUDDASSAR AND AHSAN ALI
NEW INTEGRAL INEQUALITIES THROUGH GENERALIZED CONVEX FUNCTIONS WITH APPLICATION rxiv:138.3954v1 [th.ca] 19 Aug 213 MUHAMMAD MUDDASSAR AND AHSAN ALI Abstrct. In this pper, we estblish vrious inequlities
More informationJournal of Inequalities in Pure and Applied Mathematics
Journl of Inequlities in Pure nd Applied Mthemtics http://jipm.vu.edu.u/ Volume 3, Issue, Article 4, 00 ON AN IDENTITY FOR THE CHEBYCHEV FUNCTIONAL AND SOME RAMIFICATIONS P. CERONE SCHOOL OF COMMUNICATIONS
More informationON NEW INEQUALITIES OF SIMPSON S TYPE FOR FUNCTIONS WHOSE SECOND DERIVATIVES ABSOLUTE VALUES ARE CONVEX.
ON NEW INEQUALITIES OF SIMPSON S TYPE FOR FUNCTIONS WHOSE SECOND DERIVATIVES ABSOLUTE VALUES ARE CONVEX. MEHMET ZEKI SARIKAYA?, ERHAN. SET, AND M. EMIN OZDEMIR Asrc. In his noe, we oin new some ineuliies
More informationCommunications inmathematicalanalysis Volume 6, Number 2, pp (2009) ISSN
Communictions inmthemticlanlysis Volume 6, Number, pp. 33 41 009) ISSN 1938-9787 www.commun-mth-nl.org A SHARP GRÜSS TYPE INEQUALITY ON TIME SCALES AND APPLICATION TO THE SHARP OSTROWSKI-GRÜSS INEQUALITY
More informationMath 32B Discussion Session Week 8 Notes February 28 and March 2, f(b) f(a) = f (t)dt (1)
Green s Theorem Mth 3B isussion Session Week 8 Notes Februry 8 nd Mrh, 7 Very shortly fter you lerned how to integrte single-vrible funtions, you lerned the Fundmentl Theorem of lulus the wy most integrtion
More informationCzechoslovak Mathematical Journal, 55 (130) (2005), , Abbotsford. 1. Introduction
Czechoslovk Mthemticl Journl, 55 (130) (2005), 933 940 ESTIMATES OF THE REMAINDER IN TAYLOR S THEOREM USING THE HENSTOCK-KURZWEIL INTEGRAL, Abbotsford (Received Jnury 22, 2003) Abstrct. When rel-vlued
More informationINEQUALITIES FOR TWO SPECIFIC CLASSES OF FUNCTIONS USING CHEBYSHEV FUNCTIONAL. Mohammad Masjed-Jamei
Fculty of Sciences nd Mthemtics University of Niš Seri Aville t: http://www.pmf.ni.c.rs/filomt Filomt 25:4 20) 53 63 DOI: 0.2298/FIL0453M INEQUALITIES FOR TWO SPECIFIC CLASSES OF FUNCTIONS USING CHEBYSHEV
More information0 N. S. BARNETT AND S. S. DRAGOMIR Using Gruss' integrl inequlity, the following pertured trpezoid inequlity in terms of the upper nd lower ounds of t
TAMKANG JOURNAL OF MATHEMATICS Volume 33, Numer, Summer 00 ON THE PERTURBED TRAPEZOID FORMULA N. S. BARNETT AND S. S. DRAGOMIR Astrct. Some inequlities relted to the pertured trpezoid formul re given.
More informationRIEMANN-LIOUVILLE AND CAPUTO FRACTIONAL APPROXIMATION OF CSISZAR S f DIVERGENCE
SARAJEVO JOURNAL OF MATHEMATICS Vol.5 (17 (2009, 3 12 RIEMANN-LIOUVILLE AND CAPUTO FRACTIONAL APPROIMATION OF CSISZAR S f DIVERGENCE GEORGE A. ANASTASSIOU Abstrct. Here re estblished vrious tight probbilistic
More informationHermite-Hadamard and Simpson-like Type Inequalities for Differentiable p-quasi-convex Functions
Filomt 3:9 7 5945 5953 htts://doi.org/.98/fil79945i Pulished y Fculty of Sciences nd Mthemtics University of Niš Seri Aville t: htt://www.mf.ni.c.rs/filomt Hermite-Hdmrd nd Simson-like Tye Ineulities for
More informationINEQUALITIES FOR GENERALIZED WEIGHTED MEAN VALUES OF CONVEX FUNCTION
INEQUALITIES FOR GENERALIZED WEIGHTED MEAN VALUES OF CONVEX FUNCTION BAI-NI GUO AND FENG QI Abstrct. In the rticle, using the Tchebycheff s integrl inequlity, the suitble properties of double integrl nd
More informationOn the Generalized Weighted Quasi-Arithmetic Integral Mean 1
Int. Journl of Mth. Anlysis, Vol. 7, 2013, no. 41, 2039-2048 HIKARI Ltd, www.m-hikri.com http://dx.doi.org/10.12988/ijm.2013.3499 On the Generlized Weighted Qusi-Arithmetic Integrl Men 1 Hui Sun School
More informationWEIGHTED INTEGRAL INEQUALITIES OF OSTROWSKI, 1 (b a) 2. f(t)g(t)dt. provided that there exists the real numbers m; M; n; N such that
Preprints (www.preprints.org) NOT PEER-REVIEWED Posted 6 June 8 doi.944/preprints86.4.v WEIGHTED INTEGRAL INEQUALITIES OF OSTROWSKI, µcebyšev AND LUPAŞ TYPE WITH APPLICATIONS SILVESTRU SEVER DRAGOMIR Abstrct.
More informationarxiv: v1 [math.ca] 21 Aug 2018
rxiv:1808.07159v1 [mth.ca] 1 Aug 018 Clulus on Dul Rel Numbers Keqin Liu Deprtment of Mthemtis The University of British Columbi Vnouver, BC Cnd, V6T 1Z Augest, 018 Abstrt We present the bsi theory of
More informationPart 4. Integration (with Proofs)
Prt 4. Integrtion (with Proofs) 4.1 Definition Definition A prtition P of [, b] is finite set of points {x 0, x 1,..., x n } with = x 0 < x 1
More informationON THE OSTROWSKI-GRÜSS TYPE INEQUALITY FOR TWICE DIFFERENTIABLE FUNCTIONS
Hceepe Journl of Mhemics nd Sisics Volume 45) 0), 65 655 ON THE OSTROWSKI-GRÜSS TYPE INEQUALITY FOR TWICE DIFFERENTIABLE FUNCTIONS M Emin Özdemir, Ahme Ock Akdemir nd Erhn Se Received 6:06:0 : Acceped
More informationSection 4.4. Green s Theorem
The Clulus of Funtions of Severl Vriles Setion 4.4 Green s Theorem Green s theorem is n exmple from fmily of theorems whih onnet line integrls (nd their higher-dimensionl nlogues) with the definite integrls
More informationGeneralized Hermite-Hadamard-Fejer type inequalities for GA-convex functions via Fractional integral
DOI 763/s4956-6-4- Moroccn J Pure nd Appl AnlMJPAA) Volume ), 6, Pges 34 46 ISSN: 35-87 RESEARCH ARTICLE Generlized Hermite-Hdmrd-Fejer type inequlities for GA-conve functions vi Frctionl integrl I mdt
More information