New integral inequalities for Atangana–Baleanu fractional integrals via (h, m)-convex functions

Nápoles Valdés J. E., Bayraktar B.

in: Fixed Point Theory and Functional Analysis: Metric Spaces, Banach Spaces, Hilbert Spaces, Walter De Gruyter Gmbh, pp.263-282, 2026 identifier

  • Publication Type: Book Chapter / Chapter Research Book
  • Publication Date: 2026
  • Doi Number: 10.1515/9783112215760-014
  • Publisher: Walter De Gruyter Gmbh
  • Page Numbers: pp.263-282
  • Keywords: (h, m)-convex modified functions, Atangana–Baleanu integral, Caputo–Fabrizio fractional integral, Convexity, Hermite–Hadamard inequality, Hölder inequality
  • Bursa Uludag University Affiliated: Yes

Abstract

In this article, some integral inequalities of the Hermite–Hadamard type are obtained for functions with second derivative in the class of functions modified (h, m)convex of the second type, via integrals of the Atangana–Baleanu type. Throughout the manuscript, we show that several results known from the literature are particular cases of ours.