Hermite–Hadamard-Type Integral Inequalities for Functions Whose First Derivatives are Convex

Abstract

In the paper, the authors establish some new Hermite-Hadamard type inequalities for functions whose first derivatives are of convexity and apply these inequalities to construct inequalities of special means.

On The Hermite- Hadamard-Fejér Type Integral Inequality for Convex Function

“…The most well-known inequalities related to the integral mean of a convex function are the Hermite Hadamard inequalities or its weighted versions, the so-called HermiteHadamardFejér inequalities (see, [8,13,14,15,16,19,20]). In [7], Fejer gave a weighted generalizatinon of the inequalities (1.1) as the following: …”

New Hermite Hadamard type inequalities for twice differentiable convex mappings via Green function and applications

“…Substituting the equalities (15) and (16) in (14), we obtain the inequality (13) which completes the proof.…”

“…Hermite Hadamard's inequality (1), for example, is significant in its rich geometry and hence there are many studies on it to demonstrate its new proofs, refinements, extensions and generalizations. You can check ( [1], [2], [4], [5] and [10]- [15]) and the references included there.…”

Integral inequalities of extended Simpson type for (alpha,m)-varepsilon-convex functions

“…For more information on this topic, please refer to the papers [3,5,6,9,10,[12][13][14][15] and closely-related references therein.…”