Marcela V. Mihai

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.

On bounds involving k -Appell’s hypergeometric functions

In this paper, we derive a new extension of Hermite-Hadamard’s inequality via k-Riemann-Liouville fractional integrals. Two new k-fractional integral identities are also derived. Then, using these identities as an auxiliary result, we obtain some new k-fractional bounds which involve k-Appell’s hypergeometric functions. These bounds can be viewed as new k-fractional estimations of trapezoidal and mid-point type inequalities. These results are obtained for the functions which have the harmonic convexity property. We also discuss some special cases which can be deduced from the main results of the paper.

Generalized Coordinated Nonconvex Functions and Integral Inequalities

In this section, we shall briefly introduce some recent studies of the subject. We discuss some previously known concepts and results. These preliminaries help the readers to understand the main results of the paper. Before proceeding let us recall the classical convexity on coordinates, which is also known as two dimensional classical convexity. Dragomir [ 7] was the first to investigate this extension of classical convexity in connection with integral inequalities. Let us consider a bidimensional interval Ω = [a,b]× [c,d]⊂ R2 with a< b andc < d. A function F : Ω → R is said to be convex function onΩ , if the following inequality

Conformable fractional Hermite-Hadamard inequalities via preinvex functions

Abstract The aim of this paper is to obtain some new refinements of Hermite-Hadamard type inequalities via conformable fractional integrals. The class of functions used for deriving the inequalities have the preinvexity property. We also discuss some special cases.

Fractional Hermite-Hadamard inequalities containing generalized Mittag-Leffler function

The objective of this paper is to establish some new refinements of fractional Hermite-Hadamard inequalities via a harmonically convex function with a kernel containing the generalized Mittag-Leffler function.