Generalization and reverses of the left Fejer inequality for convex functions

Abstract

In this paper we establish a generalization of the left Fejér inequality for general Lebesgue integral on measurable spaces as well as various upper bounds for the differenceis an integrable weight. Applications for discrete means and Hermite-Hadamard type inequalities are also provided.

Novel Results on Hermite–Hadamard Kind Inequalities for $$\eta $$-Convex Functions by Means of (k, r)-Fractional Integral Operators

“…Result (2) was proved by Hadamard in 1893 [6] and is celebrated in the literature as the Hermite-Hadamard integral inequality for convex functions [2]. Along the years, it has been extended to different classes of convex functions: see, e.g., [3,8,15] and references therein. In 2016, the so called ϕ-convexity was introduced [5], subsequently denoted as η-convexity [4,12].…”