Muhammad Uzair Awan

On some inequalities for relative semi-convex functions

We consider and study a new class of convex functions that are called relative semi-convex functions. Some Hermite-Hadamard inequalities for the relative semi-convex function and its variant forms are derived. Several special cases are also discussed. Results proved in this paper may stimulate further research in this area.MSC:26D15, 26A51, 49J40.

Some integral inequalities for harmonic h-convex functions involving hypergeometric functions

The aim of this paper is to establish some new Hermite-Hadamard type inequalities for harmonic h-convex functions involving hypergeometric functions. We also discuss some new and known special cases, which can be deduced from our results. The ideas and techniques of this paper may inspire further research in this field.

Integral inequalities for coordinated Harmonically convex functions

In this paper, we introduce the notion of coordinated harmonically convex functions. We derive some new integral inequalities of Hermite–Hadamard type for coordinated Harmonically convex functions. The interested readers are encouraged to find the applications of harmonically convex functions in pure and applied sciences.

Some quantum estimates for Hermite-Hadamard inequalities

In this paper, we establish quantum analogue of classical integral identity. Using this identity, we derive some quantum estimates for Hermite-Hadamard inequalities for q-differentiable convex functions and q-differentiable quasi convex functions. Results obtained present refinement and improvement of the known results. The ideas and techniques of this paper may stimulate further research.

Some quantum integral inequalities via preinvex functions

In this paper, we obtain some new quantum analogues of Hermite-Hadamard and Iyengar type inequalities for some classes of preinvex functions. Some special cases are also discussed.

Some Hermite–Hadamard type inequalities for log-h-convex functions

Abstract In the paper, the authors introduce a notion “log -h-convex functions” and establish several Hermite–Hadamard type integral inequalities for this kind of functions.

Quantum Analogues of Hermite–Hadamard Type Inequalities for Generalized Convexity

In this chapter, we discuss quantum calculus and generalized convexity. We briefly discuss some basic concepts and results regarding quantum calculus. Some quantum analogues of derivatives and integrals on finite intervals are discussed. After this we move towards generalized convexity. Examples are given to illustrate the importance and significance of generalized convex sets and generalized convex functions. We establish some quantum Hermite–Hadamard inequalities for generalized convexity. Results proved in this paper may stimulate further research activities.

Integral inequalities of Hermite–Hadamard type for logarithmically h-preinvex functions

In the paper, the authors introduce the notion “logarithmically h-preinvex functions”, reveal that the class of h-preinvex functions include several new and known classes of preinvex functions, and establish several integral inequalities of Hermite–Hadamard type.

Bounds having Riemann type quantum integrals via strongly convex functions

The aim of this paper is to obtain some new bounds having Riemann type quantum integrals within the class of strongly convex functions. The results obtained are sharp on limit q → 1. These new results reduce to Tariboon-Ntouyas, Merentes-Nikodem and other previously known results when q → 1, where 0 < q < 1. The sharpness of the results of Tariboon-Ntouyas and Merentes-Nikodem is proved as a consequence.

Fractional Hermite-Hadmard inequalities for convex functions and applications

Abstract In this paper, we derive a new lemma including third-order derivative of a function via fractional integrals. Using this lemma, we establish some new fractional estimates for Hermite-Hadamard type inequalities for convex functions. Several special cases are also discussed. Some applications to special means of real numbers are also discussed. The ideas and techniques used in this paper may stimulate future investigations regarding Hermite-Hadamard type of inequalities and its application in different areas.