On Generalized Strongly Convex Functions and Unified Integral Operators

Timing Yu,Chahn Yong Jung,Ghulam Farid,Kahkashan Mahreen,Soo Hak Shim,Ghulam Mustafa

doi:10.1155/2021/6695781

Abstract

In this paper, we define a strongly exponentially α , h − m -convex function that generates several kinds of strongly convex and convex functions. The left and right unified integral operators of these functions satisfy some integral inequalities which are directly related to many unified and fractional integral inequalities. From the results of this paper, one can obtain various fractional integral operator inequalities that already exist in the literature.

Highlights

Mathematical inequalities are very important and useful in the study of various kinds of problems in mathematics, operation research, economics, physics, and engineering and in many other subjects of diverse fields
Mathematical inequalities for different kinds of fractional integrals are in the focus of researchers, and a lot of papers have been published on this subject
We give the definition of a new function called the strongly exponentially (α, h − m)-convex function

Summary

Introduction

Mathematical inequalities are very important and useful in the study of various kinds of problems in mathematics, operation research, economics, physics, and engineering and in many other subjects of diverse fields. We give recently established results in [26] for the fractional integral operators containing the extended generalized Mittag-Leffler function defined in [7] by utilizing (α, h − m)-convex functions. If f is differentiable and |f′| is (α, h − m)-convex, (α, m) ∈ [0, 1]2, m ≠ 0, for α′, β ≥ 1, the following fractional integral inequality for generalized fractional integral operators holds: E following results are proved for unified integral operators of strongly convex functions in [39].

Results

Conclusion