Hermite-Hadamard and Hermite-Hadamard-Fejer type inequalities for \(p\)-convex functions via new fractional conformable integral operators

Volume 19, Issue 4, pp 230--240 http://dx.doi.org/10.22436/jmcs.019.04.02

Publication Date: June 14, 2019 Submission Date: June 02, 2018 Revision Date: November 23, 2018 Accteptance Date: December 20, 2018

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Authors

Naila Mehreen - School of Natural Sciences, National University of Sciences and Technology, H-12 Islamabad, Pakistan. Matloob Anwar - School of Natural Sciences, National University of Sciences and Technology, H-12 Islamabad, Pakistan.

Abstract

In this paper, we obtained the Hermite-Hadamard and Hermite-Hadamard-Fejer type inequalities for \(p\)-convex functions via new fractional conformable integral operators. We also gave some new Hermite-Hadamard and Hermite-Hadamard-Fejer type inequalities for convex functions and harmonically convex functions via new fractional conformable integral operators.

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Keywords

• Hermite-Hadamard inequalities
• Hermite-Hadamard-Fejer inequalities
• Riemann-Liouville fractional integral
• fractional conformable integral operators
• convex functions
• \(p\)-convex functions
• harmonically convex functions

MSC

•  26A51
•  26A33
•  26D10
•  26D07
•  26D15

References

• [1] M. U. Awan, M. A. Noor, M. V. Mihai, K. I. Noor, Inequalities via harmonic convex functions: Conformable fractional calculus approach, J. Math. Inequal., 12 (2008), 143--153
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [2] F. Chen, Extension of the Hermite-Hadamard inequality for harmonicaly convex functions via fractional integrals, Appl. Math. Comut., 268 (2015), 121--128
  • View Article
  • Google Scholar


• [3] H. Chen, U. N. Katugampola, Katugampola, Hermite--Hadamard and Hermite--Hadamard--Fejer type inequalities for generalizes fractional integrals, J. Math. Anal. Appl., 446 (2017), 1274--1291
  • View Article
  • Google Scholar


• [4] L. Fejer, Über die Fourierreihen, II, Math. Naturwise. Anz Ungar. Akad. Wiss., 24 (1906), 369--390
  • View Article


• [5] J. Hadamard, Étude sur les propriétés des fonctions entières et en particulier d'une fonction considérée par Riemann, J. Math. Pures Appl., 58 (1893), 171--215
  • View Article
  • MathSciNet
  • Google Scholar


• [6] I. Işcan, Hermite-Hadamard-Fejer type inequalities for convex functions via fractional integrals, arXiv, 2014 (2014), 10 pages
  • View Article
  • Google Scholar


• [7] I. Işcan, Hermite-Hadamard type inequalities for $p$-convex functions, Int. J. Anal. Appl., 11 (2016), 137--145
  • View Article
  • Google Scholar
  • MATH


• [8] I. Işcan, S. H. Wu, Hermite-Hadamard type inequalities for harmonically convex functions via fractional integrals, Appl. Math. Comput., 238 (2014), 237--244
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [9] F. Jarad, E. Uğurlu, T. Abdeljawad, D. Baleanu, On a new class of fractional operators, Adv. Difference Equ., 2017 (2017), 16 pages
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [10] U. N. Katugampola, New approach to generalized fractional derivatives, Bull. Math. Anal. Appl., 6 (2014), 1--15
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [11] A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations, Elsevier Science B. V., Amsterdam (2006)
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [12] M. Kunt, I. Işcan, Hermite-Hadamard-Fejér type inequalities for $p$-convex functions, Arab. J. Math. Sci., 23 (2017), 215--230
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [13] M. Kunt, I. Işcan, Hermite-Hadamard-Fejér type inequalities for $p$-convex functions via fractional integrals, Iran. J. Sci. Technol. Trans. A Sci., 42 (2018), 2079--2089
  • View Article
  • MathSciNet
  • Google Scholar


• [14] S. G. Samko, A. A. Kilbas, O. I. Marichev, Fractional Integrals and Derivatives, Gordon and Breach Science Publishers, Yverdon (1993)
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [15] M. Z. Sarikaya, E. Set, H. Yaldiz, N. Başak, Hermite-Hadamard's inequlities for fractional integrals and related fractional inequalitis, Math. Comput. Modelling, 57 (2013), 2403--2407
  • View Article
  • Google Scholar


• [16] E. Set, A. O. Akdemir, I. Mumcu, The Hermite--Hadamard's inequality and its extentions for conformable fractioanal integrals of any order $\alpha>0$, preprint, 2016 (2016), 13 pages
  • View Article
  • Google Scholar


• [17] E. Set, J. Choi, A. Gözpınar, Hermite-Hadamard type inequalities for new fractional conformable integral operators, preprint, 2018 (2018), 7 pages
  • View Article
  • Google Scholar


• [18] E. Set, M. E. Özdemir, S. S. Dragomir, On Hadamard-type inequalities involving seversl kinds of convexity, J. Inequal. Appl., 2010 (2010), 12 pages
  • View Article
  • Google Scholar


• [19] E. Set, M. Z. Sarikaya, A. Gözpınarc, Some Hermite--Hadamard type inequalities for convex functions via conformable fractional integrals and related inequalities, Creat. Math. Inform., 26 (2016), 221--229
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [20] E. Set, M. Z. Sarikaya, M. E. Özdemir, H. Yaldirm, The Hermite--Hadamard's inequality for some convex functions via fractional integrals and related results, J. Appl. Math. Stat. Inform., 10 (2014), 69--83
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [21] G. H. Toader, Some generalizations of the convexity, Proc. Colloq. Approx. Optim (Cluj-Napoca, Romania), 1985 (1985), 329--338
  • MathSciNet
  • Google Scholar
  • MATH