IMPROVEMENT OF FRACTIONAL HERMITE- HADAMARD TYPE INEQUALITY FOR CONVEX FUNCTIONS


KUNT M. , İŞCAN İ., TURHAN S., KARAPINAR D.

MISKOLC MATHEMATICAL NOTES, vol.19, no.2, pp.1007-1017, 2018 (Journal Indexed in SCI) identifier

  • Publication Type: Article / Article
  • Volume: 19 Issue: 2
  • Publication Date: 2018
  • Doi Number: 10.18514/mmn.2018.2441
  • Title of Journal : MISKOLC MATHEMATICAL NOTES
  • Page Numbers: pp.1007-1017
  • Keywords: convex functions, Hermite-Hadamard inequalities, Riemann-Liouville fractional integrals, midpoint type inequalities

Abstract

In this paper, it is proved that fractional Hermite-Hadamard inequality and fractional Hermite-Hadamard-Fejer inequality are just results of Hermite-Hadamard-Fejer inequality. After this, a new fractional Hermite-Hadamard inequality which is not a result of Hermite-Hadamard-Fejer inequality and better than given in [9] by Sarikaya et al. is obtained. Also, a new equality is proved and some new fractional midpoint type inequalities are given. Our results generalizes the results given in [5] by Kirmaci.