Generalized Hermite–Hadamard-Type Integral Inequalities forh-Godunova–Levin Functions

Rana Safdar Ali,Gauhar Rahman,Jihad Younis,Shahid Mubeen,Sabila Ali,Asad Ali,Umair Ali

doi:10.1155/2022/9113745

Abstract

The main objective of this article is to establish generalized fractional Hermite–Hadamard and related type integral inequalities forh-Godunova–Levin convexity andh-Godunova–Levin preinvexity with extended Wright generalized Bessel function acting as kernel. Moreover, Hermite–Hadamard-type and trapezoid-type inequalities for several known convexities including Godunova–Levin function, classical convex,s-Godunova–Levin function,P-function, ands-convex function are deduced as corollaries. These obtained results are analyzed in the form of generalization of fractional inequalities.

Highlights

Many inequalities have been extensively analyzed and reported in research fields as a result of convexity and its generalizations in engineering and sciences [12–25]
The concept of convexity has been extended to s-Godunova–Levin type of convexity by Dragomir [32]
We have considered h-Godunova–Levin convex and h-Godunova–Levin preinvex function to obtain generalized fractional version of Hermite–Hadamard-type inequality and trapezoid-type inequalities related to Hermite–Hadamard inequality

Summary

Introduction

Many inequalities have been extensively analyzed and reported in research fields as a result of convexity and its generalizations in engineering and sciences [12–25]. E generalized fractional integral operators, with extended generalized Bessel–Maitland function as kernel, are defined, for μ, ], η, ρ, c, c ∈ C, R(μ) > 0, R(]) ≥ − 1, R(η) > 0, R(ρ) > 0, R(c) > 0, ξ, m, σ ≥ 0, and m, ξ > R(μ) + σ, as follows: x μ,ξ,m,σ,c ],η,ρ,c;p+ We obtain Hermite–Hadamard- and trapezoid-type inequalities using the generalized fractional integral operator with extended generalized Bessel–Maitland function as its nonsingular kernel.

Results

Conclusion