On the refinements of the Hermite-Hadamard inequality (original) (raw)

Some Results on Hermite-Hadamard Type Inequality through Convexity

Turkish Journal of Analysis and Number Theory, 2014

Our aim in this article to establish various inequalities for some differentiable mapping that are connected with illustrious Hermite-Hadamard integral inequality for mapping whose absolute values of derivatives are convex. The new integral inequalities are then applied to some special means and as well as numerical integration to obtain some better estimates.

GENERALISATIONS OF INTEGRAL INEQUALITIES OF HERMITE{--}HADAMARD TYPE THROUGH CONVEXITY

In this paper, we establish various inequalities for some differentiable mappings that are linked with the illustrious Hermite-Hadamard integral inequality for mappings whose derivatives are s-(α, m)-convex. The generalised integral inequalities contribute better estimates than some already presented. The inequalities are then applied to numerical integration and some special means.

Some generalizations of Hermite–Hadamard type inequalities

SpringerPlus, 2016

Introduction and preliminaries This paper generalizes some well-known results for Hermite-Hadamard integral inequality by generalizing the convex function factor of the integrand to be an η-convex function. The obtained results have as particular cases those previously obtained for convex functions in the integrand. The following inequality is well known in the literature as the Hermite-Hadamard integral inequality (

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

Turkish Journal of Analysis and Number Theory, 2014

In this paper, we extend some estimates of the right hand side of a Hermite-Hadamard-Fejér type inequality for functions whose first derivatives absolute values are convex. The results presented here would provide extensions of those given in earlier works.