On Hadamard inequalities for refined convex functions via strictly monotone functions-Reference-Cited by-同舟云学术

On Hadamard inequalities for refined convex functions via strictly monotone functions

Published:2022 Issue:11 Volume:7 Page:20043-20057
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Zahra Moquddsa¹,Abuzaid Dina²,Farid Ghulam³,Nonlaopon Kamsing⁴

Affiliation:

1. Department of Mathematics, University of Wah, Wah Cantt, Pakistan

2. Department of Mathematics, King Abdul Aziz University, Saudi Arabia

3. Department of Mathematics, COMSATS University Islamabad, Attock Campus, Pakistan

4. Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand

Abstract

<abstract><p>In this paper, we define refined $ (\alpha, h-m) $-convex function with respect to a strictly monotone function. This function provides refinements of various well-known classes of functions for specific strictly monotone functions. By applying definition of this new function we prove the Hadamard inequalities for Riemann-Liouville fractional integrals. These inequalities give the refinements of fractional Hadamard inequalities for convex, $ (\alpha, m) $-convex, $ (h-m) $-convex, $ (s, m) $-convex, $ h $-convex and many other related well-known classes of functions implicitly. Also, Hadamard type inequalities for $ k $-fractional integrals are given.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

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