Novel results on Hermite-Hadamard kind inequalities for $η$-convex functions by means of $(k,r)$-fractional integral operators

Eze R. Nwaeze; Delfim F. M. Torres

doi:10.1007/978-981-13-3013-1_16

paper

Novel results on Hermite-Hadamard kind inequalities for $η$ -convex functions by means of $(k, r)$ -fractional integral operators

arXiv:1802.05619 · doi:10.1007/978-981-13-3013-1_16

Abstract

We establish new integral inequalities of Hermite-Hadamard type for the recent class of $η$ -convex functions. This is done via generalized $(k, r)$ -Riemann-Liouville fractional integral operators. Our results generalize some known theorems in the literature. By choosing different values for the parameters $k$ and $r$ , one obtains interesting new results.

This is a preprint of a paper whose final and definite form is a Springer chapter in the Book 'Advances in Mathematical Inequalities and Applications', published under the Birkhauser series 'Trends in Mathematics', ISSN: 2297-0215 [see http://www.springer.com/series/4961]. Submitted 02-Jan-2018; Revised 10-Jan-2018; Accepted 13-Feb-2018

Novel results on Hermite-Hadamard kind inequalities for η-convex functions by means of (k,r)-fractional integral operators

Abstract

Novel results on Hermite-Hadamard kind inequalities for $η$ -convex functions by means of $(k, r)$ -fractional integral operators