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 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 69 Issue: 4
  • Publication Date: 2019
  • Doi Number: 10.1515/ms-2017-0261
  • Journal Name: MATHEMATICA SLOVACA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.773-784
  • Keywords: convex functions, Hermite-Hadamard inequalities, left Riemann-Liouville fractional integral, trapezoid type inequalities, midpoint type inequalities, DIFFERENTIABLE MAPPINGS
  • Karadeniz Technical University Affiliated: Yes

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.