Improvements of Logarithmic and Identric Mean Inequalities for Scalars and Operators (original) (raw)

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.

On the refinements of the Hermite-Hadamard inequality

Journal of Inequalities and Applications, 2012

In this paper, we present some refinements of the classical Hermite-Hadamard integral inequality for convex functions. Further, we give the concept of n-exponential convexity and log-convexity of the functions associated with the linear functionals defined by these inequalities and prove monotonicity property of the generalized Cauchy means obtained via these functionals. Finally, we give several examples of the families of functions for which the results can be applied. MSC: 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.