REFINEMENTS OF THE HERMITE-HADAMARD INEQUALITY FOR CONVEX FUNCTIONS (original) (raw)

New inequalities of hermite-hadamard type for convex functions with applications

Journal of Inequalities and Applications, 2011

In this paper, some new inequalities of the Hermite-Hadamard type for functions whose modulus of the derivatives are convex and applications for special means are given. Finally, some error estimates for the trapezoidal formula are obtained. 2000 Mathematics Subject Classiffication. 26A51, 26D10, 26D15.

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.

Refinements of Generalised Hermite-Hadamard Inequality

Bulletin des Sciences Mathématiques, 2023

New insights, improvements, and refinements of the well known Hermite-Hadamard inequality are established for a general class of convex functions. Inequalities involving products of two harmonically h-s functions are also obtained.

Some estimates on the Hermite-Hadamard inequality through geometrically quasi-convex functions

Miskolc Mathematical Notes, 2017

In present paper, by proving a new integral identity, using Hölder's inequality and mathematical analysis, we prove some Hermite-Hadamard type integral inequalities for geometrically quasi-convex functions which give better estimates to those already proven for the rightside of a Hermite-Hadamard type inequality established for geometrically convex functions in earlier works. A numerical example is also provided to support our claim. Applications of the results to special means of positive real numbers are given.

Some New Hermite-Hadamard Type Inequalities for Convex Functions

2020

Convex sets and convex functions play a fundamental role in the development of various fields of pure and applied mathematics. Recently, many new generalizations of inequalities with respect to Hermite-Hadamard have been proposed in the literature. In this paper, some new inequalities of the Hermite-Hadamard type for differentiable convex functions are given. These new inequalities are based on the second derivative functions.

The Hermite–Hadamard inequality for log-convex functions

Nonlinear Analysis: Theory, Methods & Applications, 2012

We discuss the existence of a strengthening of Hermite-Hadamard inequality in the case of log-convex functions. Unlike the classical case, which belongs to the …eld of linear functional analysis, this analogue involves nonlinear means such as the geometric mean and the logarithmic mean.