THE LEFT RIEMANN-LIOUVILLE FRACTIONAL HERMITE-HADAMARD TYPE INEQUALITIES FOR CONVEX FUNCTIONS


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

MATHEMATICA SLOVACA, vol.69, no.4, pp.773-784, 2019 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 69 Issue: 4
  • Publication Date: 2019
  • Doi Number: 10.1515/ms-2017-0261
  • Title of Journal : MATHEMATICA SLOVACA
  • Page Numbers: pp.773-784
  • Keywords: convex functions, Hermite-Hadamard inequalities, left Riemann-Liouville fractional integral, trapezoid type inequalities, midpoint type inequalities, DIFFERENTIABLE MAPPINGS

Abstract

In this paper, with a new approach, a new fractional Hermite-Hadamard type inequalities for convex functions is obtained by using only the left Riemann-Liouville fractional integral. Also, to have new fractional trapezoid and midpoint type inequalities for the differentiable convex functions, two new equalities are proved. Our results generalize earlier studies. We expect that this study will be lead to the new fractional integration studies for Hermite-Hadamard type inequalities.