Generalizations of fractional Hermite-Hadamard-Mercer like inequalities for convex functions

Vivas-Cortez M., Ali M. A., Kashuri A., Budak H.

AIMS MATHEMATICS, no.9, pp.9397-9421, 2021 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Publication Date: 2021
  • Doi Number: 10.3934/math.2021546
  • Journal Name: AIMS MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Directory of Open Access Journals
  • Page Numbers: pp.9397-9421
  • Kocaeli University Affiliated: No

Abstract

In this work, we establish inequalities of Hermite-Hadamard-Mercer (HHM) type for convex functions by using generalized fractional integrals. The results of our paper are the extensions and refinements of Hermite-Hadamard (HH) and Hermite-Hadamard-Mercer (HHM) type inequalities. We discuss special cases of our main results and give new inequalities of HH and HHM type for different fractional integrals like, Riemann-Liouville (RL) fractional integrals, k-Riemann-Liouville (k-RL) fractional integrals, conformable fractional integrals and fractional integrals of exponential kernel.