Harmonic Beta-Preinvex Functions and Inequalities

Abstract

In this paper, we introduce and study a new class of harmonic convex functions which is called harmonic beta-preinvex functions. We establish some estimates, involving the Euler Beta function and the Hypergeometric function of the integral $\int_a^{a+\eta(b,a)}(x-a)^p(a+\eta(b,a)-x)^qf(x)\mathrm{d}x$ for the class of functions whose certain powers of the absolute value are generalized harmonic preinvex function. Some special cases are also discussed. Results obtained in this paper can be viewed as significant contribution in this fascinating and dynamic field.