Tbilisi Mathematical Journal

Conformable fractional Hermite-Hadamard inequalities via preinvex functions

Muhammad Uzair Awan, Muhammad Aslam Noor, Marcela V. Mihai, and Khalida Inayat Noor

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

The aim of this paper is to obtain some new refinements of Hermite-Hadamard type inequalities via conformable fractional integrals. The class of functions used for deriving the inequalities have the preinvexity property. We also discuss some special cases.

Article information

Source
Tbilisi Math. J., Volume 10, Issue 4 (2017), 129-141.

Dates
Received: 10 April 2016
Accepted: 6 September 2017
First available in Project Euclid: 21 April 2018

Permanent link to this document
https://projecteuclid.org/euclid.tbilisi/1524276063

Digital Object Identifier
doi:10.1515/tmj-2017-0051

Mathematical Reviews number (MathSciNet)
MR3731396

Zentralblatt MATH identifier
1377.26023

Subjects
Primary: 26D15: Inequalities for sums, series and integrals
Secondary: 26A51: Convexity, generalizations 26A33: Fractional derivatives and integrals

Keywords
convex preinvex fractional conformable Hermite-Hadamard

Citation

Awan, Muhammad Uzair; Noor, Muhammad Aslam; Mihai, Marcela V.; Noor, Khalida Inayat. Conformable fractional Hermite-Hadamard inequalities via preinvex functions. Tbilisi Math. J. 10 (2017), no. 4, 129--141. doi:10.1515/tmj-2017-0051. https://projecteuclid.org/euclid.tbilisi/1524276063


Export citation

References

  • T. Abdeljawad, On conformable fractional calculus, J. Comput. Appl. Math., 279(2015), 57-66.
  • G. Cristescu and L. Lupsa, Non-connected Convexities and Applications, Kluwer Academic Publishers, Dordrecht, Holland, 2002.
  • S. S. Dragomir and R. P. Agarwal, Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula, Appl. Math. Lett. 11 (1998), 91–95.
  • S. S. Dragomir and C. E. M. Pearce, Selected topics on Hermite-Hadamard inequalities and applications, Victoria University, 2000.
  • M. A. Hanson, On Sufficiency of the Kuhn-Tucker Conditions, J. Math. Anal. Appl. 80(1981), 545–550.
  • R. Khalil, M. Al Horani, A. Yousef, M. Sababheh, A new definition of fractional derivative, J. Computat. Appl. Math., 264(2014), 65–70.
  • K. S. Miller and B. Ross, An introduction to the fractional calculus and fractional differential equations, New York: Wiley, 1993.
  • S. Mititelu, Invex Sets, Stud. Cerc. Mat., 46(5) (1994), 529–532.
  • S. R. Mohan and S. K. Neogy, On invex sets and preinvex functions, J. Math. Anal. Appl. 189(1995), 901–908.
  • M. A. Noor, K. I. Noor and M. U. Awan, Some quantum estimates for Hermite-Hadamard inequalities, Appl. Math. Comput. 251(2015) 675–679.
  • M. A. Noor, K. I. Noor and M. U. Awan, Some quantum integral inequalities via preinvex functions, Appl. Math. Comput. 269(2015) 242–251.
  • M. A. Noor, K. I. Noor, M. U. Awan and S. Khan, Hermite-Hadamard inequalities for $s$-Godunova-Levin preinvex functions, J. Adv. Math. Stud. 7(2), (2014), 12-19.
  • M. A. Noor, K. I. Noor, M. U. Awan and J. Li, On Hermite-Hadamard inequalities for $h$-Preinvex functions, Filomat 28(7), (2014), 1463-1474.
  • M. A. Noor, M. U. Awan, M. V. Mihai and K. I. Noor, Fractional Hermite-Hadamard inequalities for differentiable $s$-Godunova-Levin functions, Filomat, to appear.
  • M. Z. Sarikaya, E. Set, H. Yaldiz and N. Basak, Hermite-Hadamard's inequalities for fractional integrals and related fractional inequalities, Math. Comput. Model., 57 (2013), 2403-2407.
  • E. Set, New inequalities of Ostrowski type for mappings whose derivatives are $s$-convex in the second sense via fractional integrals, Comput. Math. Appl., 63(7), (2012), 1147–1154.
  • E. Set, A. O. Akdemir and I. Mumcu, The Hermite-Hadamard's inequality and its extentions for conformable fractioanal integrals of any order $\alpha> 0$, preprint.
  • E. Set, M. Z. Sarikaya and A. Gozpinar, Some Hermite-Hadamard type inequalities for convex functions via conformable fractional integrals and related inequalities, preprint, (2016).
  • S. Varošanec, On $h$-convexity, J. Math. Anal. Appl. 326 (2007) 303-311.
  • T. Weir and B. Mond, Preinvex functions in multiobjective optimization, J. Math. Anal. Appl. 136(1988), 29-38.