Generalization of some fractional versions of Hadamard inequalities via exponentially $ (\alpha, h-m) $-convex functions

• Published in: AIMS mathematics Vol. 6; no. 8; pp. 8978 - 8999
• Main Authors: Lv, Yu-Pei, Farid, Ghulam, Yasmeen, Hafsa, Nazeer, Waqas, Jung, Chahn Yong
• Format: Journal Article
• Language: English
• Published: AIMS Press 01-01-2021
• Subjects: exponentionally (α; hadamard inequality; h−m)-convex function; riemann-liouville fractional integrals
• ISSN: 2473-6988; 2473-6988
• DOI: 10.3934/math.2021521

In this paper we give Hadamard inequalities for exponentially (α,h−m)-convex functions using Riemann-Liouville fractional integrals for strictly increasing function. Results for Riemann-Liouville fractional integrals of convex, m-convex, s-convex, (α,m)-convex, (s,m)-convex, (h−m)-convex, (α,h−m)-convex, exponentially convex, exponentially m-convex, exponentially s-convex, exponentially (s,m)-convex, exponentially (h−m)-convex, exponentially (α,h−m)-convex functions are particular cases of the results of this paper. The error estimations of these inequalities by using two fractional integral identities are also given.