On Hadamard inequalities for refined convex functions via strictly monotone functions

AIMS Mathematics

article

Moquddsa Zahra¹  Dina Abuzaid²  Ghulam Farid³  Kamsing Nonlaopon⁴ 

[1] Department of Mathematics, University of Wah;Department of Mathematics, King Abdul Aziz University;Department of Mathematics, COMSATS University Islamabad, Attock Campus;Department of Mathematics, Faculty of Science, Khon Kaen University

关键词: convex function;    refined $ (\alpha;    h-m) $-convex function;    monotone function;    Hadamard inequality;    Riemann-Liouville fractional integrals;   

DOI  :  10.3934/math.20221096

学科分类：地球科学(综合)

来源: AIMS Press

【 摘 要 】

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.

【 授权许可】

CC BY