Some New Results on Hermite-Hadamard-Mercer-Type Inequalities Using a General Family of Fractional Integral Operators

SET E., Celik B., ÖZDEMİR M. E., Aslan M.

FRACTAL AND FRACTIONAL, vol.5, no.3, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 5 Issue: 3
  • Publication Date: 2021
  • Doi Number: 10.3390/fractalfract5030068
  • Journal Name: FRACTAL AND FRACTIONAL
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, INSPEC, Directory of Open Access Journals
  • Keywords: convex function, Hermite-Hadamard inequalities, Jensen-Mercer inequality, fractional integral operators
  • Bursa Uludag University Affiliated: Yes

Abstract

The aim of this article is to obtain new Hermite-Hadamard-Mercer-type inequalities using Raina's fractional integral operators. We present some distinct and novel fractional Hermite-Hadamard-Mercer-type inequalities for the functions whose absolute value of derivatives are convex. Our main findings are generalizations and extensions of some results that existed in the literature.