Yıl 2017, Cilt 5, Sayı 2, Sayfalar 181 - 191 2017-10-15

HERMITE-HADAMARD AND HERMITE-HADAMARD-FEJER TYPE INEQUALITIES FOR (k, h)-CONVEX FUNCTION VIA KATUGAMPOLA FRACTIONAL INTEGRALS

ERHAN SET [1] , ALİ KARAOĞLAN [2]

75 111

In this paper, we obtain some new Hermite-Hadamard and Hermite-Hadamard-Fejer type inequalities for (k,h)-convex functions via Katugampola fractionals which are a generalization of Riemann-Liouville and the Hadamard fractional integrals in to a single form.

Hermite-Hadamard-Fejer inequality, Riemann-Liouville fractional integrals, Hadamard fractional integrals, Katugampola fractional integrals, (k;h)-convex functions
  • [1] W.W. Breckner, Stetigkeitsaussagenf ureine Klass ever all gemeinerter konvexer funktionen in topologisc henlianeren Raumen, Pupl. Inst. Math., 23 (1978), 13-20.
  • [2] H. Chen, U.N. Katugampola, Hermite-Hadamard and Hermite-Hadamard-Fejer type inequalities for generalized fractional integrals, J. Math. Anal. Appl., 446 (2017), 1274-1291.
  • [3] Z. Dahmani, On Minkowski and Hermite-Hadamard integral inequalities via fractional integration, Ann. Funct. Anal., 1 (1) (2010), 51-58.
  • [4] S.S. Dragomir and S. Fitzpatrick, The Hadamard's inequality for s-convex functions in the rst sense, Demonstratio Math, 31 (3) (1998), 633-642.
  • [5] S.S. Dragomir and S. Fitzpatrick, The Hadamard's inequality for s-convex functions in the second sense, Demonstration Math, 32 (4) (1999), 687-696.
  • [6] S.S. Dragomir and C.E.M. Pearce, Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University, 2000 (Online:http:rgma.vu.edu.au/monographs)
  • [7] S.S. Dragomir, J. Pecaric , L.E. Person, Some inequalities of Hadamard type, Soochow J. Math., 21 (1995), 335-341.
  • [8] L. Fejer, Über die Fourierreihen, II, Math. Naturwiss. Anz.Ungar.Akad. Wiss., 24 (1906), 369-390.
  • [9] E.K. Godunova and V.I. Levin, Nerevenstra dlja funccii sirokogo klassa soderzassego vypuklye, monotonnye i nekotorye drugie vidy funkaii, Vycislitel Mat. i Mt. Fiz. Mezvuzov Sb. Nauc. Trudov. MPGI, Moscow, 1985, 138-142.
  • [10] H. Hudzik and L. Maligranda, Some remarks on s-convex functions, Aequationes Math., 48 (1994), 100-111.
  • [11] İ. İŞCan, Hermite-Hadamard-Fejer type inequalities for convex function via fractional integrals, Stud. Univ. Babeş-Bolyai Math., 60(2015), No.3, 355-366.
  • [12] U.N. Katugampola, New approach to a generalized fractional integrals, Appl. Math. Comput. 218 (4) (2011), 860-865.
  • [13] U.N. Katugampola, New approach to generalized fractional derivatives, Bull. Math. Anal. Appl., 6 (4) (2014), 1-15.
  • [14] U.N. Katugampola, Mellin transforms of generalized fractional integrals and derivatives, Appl. Math. Comput. 257 (2011), 566-580.
  • [15] G. Maksa, ZS. Pales, The equality case in some recent convexity inequlities, Opuscula Math. 31, 2 (2011), 269-277.
  • [16] J. Matkowski and T. Siwiatkowski, On Subadditive, Prosidings of The American Mathematical Society. 119 (1993), 187-197.
  • [17] B. Micharda and T. Rajba, On some Hermite-Hadamard-Fejer Inequalities for (k,h)-convex functions, Mathematical Inequalities and Applications 12, 4 (2012), 931-940.
  • [18] D.S. Mitrinovic and I.B. Lackovic, Hermite and convexity, Aequationes Math.28, 3 (1985), 229-232.
  • [19] W. Orlicz. A note on modular spaces. IX, Bull. Acad. Polon. Sci., Ser. Sci. Math. Astronom. Phys. 16 (1968), 801-808. MR 39:3278
  • [20] M.E.  Ozdemir, E. Set, M. Alomari, Integral inequalities via several kinds of convexity, Creat. Math. Inform., 20(1) (2011), 62-73.
  • [21] M. E. Özdemir, Ç Yıldız, A. O. Akdemir, E. Set, On some inequalities for s-convex functions and applications, J. Ineq. Appl., 2013(1) (2013), 333.
  • [22] S.G. Samko, A.A. Kilbas, O.I. Marichev, Fractional integrals and Derivatives, Theory and Applications. Gordon and Breach, Amsterdam,1993
  • [23] M.Z. Sarıkaya, E. Set, H. Yaldiz, N. Başak, Hermite-Hadamard's inequalities for fractional integrals and related fractional inequalities, Math.Comput. Modelling, 57(9) (2013) 2403-2407
  • [24] E. Set, New inequalities of Ostrowski type for mapping whose derivatives are s-convex in the second sense via fractional integrals, Computers and Math. with Appl. 63 (2012), 1147-1154.
  • [25] E. Set, İ. İşcan, M.Z. Sarıkaya, M.E. Özdemir, On new inequalities of Hermite-Hadamard Fejer type for convex functions via fractional integrals, Appl. Math. Comput., 259 (2015), 875-881.
  • [26] E. Set, A. Karaoğlan, Hermite-Hadamard-Fejer type inequalities for (k-h)-convex function via Riemann-Liouville and conformable fractional integrals, AIP Conference Proceedings, 1883(020039) (2017), 1-5.
  • [27] E. Set, M.E.  Ozdemir, M.Z. Sarıkaya, Inequalities of Hermite-Hadamards type for functions whose derivatives absolute values are m-convex, AIP Conf. Proc., 1309(1) (2010), 861-863.
  • [28] E. Set, İ. İşcan, F. Zehir, On some new inequalities of Hermite-Hadamard type involving harmonically convex functions via fractional integrals, Konuralp J. Math., 3(1) (2015), 42-55.
  • [29] E. Set, M.Z. Sarıkaya, M.E. Özdemir, H. Yıldırım The Hermite-Hadamard's inequality for some convex functions via fractional integrals and related results, J. Appl. Math. Statis. Inform., 10(2) (2014), 69-83.
  • [30] S. Varosanec. On h-convexity, J. Math. Anal. Appl., 326 (1) (2007), 303-311.
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Yazarlar

Yazar: ERHAN SET
E-posta: erhanset@yahoo.com
Ülke: Turkey


Yazar: ALİ KARAOĞLAN
E-posta: aliblackboy80@hotmail.com
Ülke: Turkey


Bibtex @araştırma makalesi { konuralpjournalmath319429, journal = {Konuralp Journal of Mathematics}, issn = {}, address = {Mehmet Zeki SARIKAYA}, year = {2017}, volume = {5}, pages = {181 - 191}, doi = {}, title = {HERMITE-HADAMARD AND HERMITE-HADAMARD-FEJER TYPE INEQUALITIES FOR (k, h)-CONVEX FUNCTION VIA KATUGAMPOLA FRACTIONAL INTEGRALS}, key = {cite}, author = {SET, ERHAN and KARAOĞLAN, ALİ} }
APA SET, E , KARAOĞLAN, A . (2017). HERMITE-HADAMARD AND HERMITE-HADAMARD-FEJER TYPE INEQUALITIES FOR (k, h)-CONVEX FUNCTION VIA KATUGAMPOLA FRACTIONAL INTEGRALS. Konuralp Journal of Mathematics, 5 (2), 181-191. Retrieved from http://dergipark.gov.tr/konuralpjournalmath/issue/28490/319429
MLA SET, E , KARAOĞLAN, A . "HERMITE-HADAMARD AND HERMITE-HADAMARD-FEJER TYPE INEQUALITIES FOR (k, h)-CONVEX FUNCTION VIA KATUGAMPOLA FRACTIONAL INTEGRALS". Konuralp Journal of Mathematics 5 (2017): 181-191 <http://dergipark.gov.tr/konuralpjournalmath/issue/28490/319429>
Chicago SET, E , KARAOĞLAN, A . "HERMITE-HADAMARD AND HERMITE-HADAMARD-FEJER TYPE INEQUALITIES FOR (k, h)-CONVEX FUNCTION VIA KATUGAMPOLA FRACTIONAL INTEGRALS". Konuralp Journal of Mathematics 5 (2017): 181-191
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