Refinements of some fractional integral inequalities for refined ( α , h − m ) $(\alpha ,h-m)$ -convex function

• Main Authors: Chahn Yong Jung, Ghulam Farid, Hafsa Yasmeen, Yu-Pei Lv, Josip Pečarić
• Format: Article
• Language: English
• Published: SpringerOpen 2021-08-01
• Series: Advances in Difference Equations
• Subjects: Refined ( α , h − m ) $(\alpha ,h-m)$ -convex function; Refined ( h − m ) $(h-m)$ -convex function; Hermite–Hadamard inequality; Riemann–Liouville fractional integrals
• Online Access: https://doi.org/10.1186/s13662-021-03544-0
• ISSN: 1687-1847

Abstract This article investigates new inequalities for generalized Riemann–Liouville fractional integrals via the refined ( α , h − m ) $(\alpha ,h-m)$ -convex function. The established results give refinements of fractional integral inequalities for ( h − m ) $(h-m)$ -convex, ( α , m ) $(\alpha ,m)$ -convex, ( s , m ) $(s,m)$ -convex, and related functions. Also, the k-fractional versions of given inequalities by using a parameter substitution are provided.