*-Hermite-Hadamard-Fejer Inequality and Some New Inequality via *-Calculus (original) (raw)

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

Old and New on the Hermite-Hadamard Inequality

Real Analysis Exchange, 2003

The goal of this paper is to describe the panorama of Mathematics grown up from the celebrated inequality of Hermite and Hadamard. Both old and new results are presented, complemented and discussed within this framework.

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.

New extensions of the Hermite-Hadamard inequality

Contributions to mathematics, 2023

Some new results related to generalized Hermite-Hadamard-type inequalities are established. For obtaining new inequalities, various approaches are utilized, including boundedness, convexity, and concavity. Considering special values of the parameters, it is demonstrated how the obtained inequalities reduce to the known ones.

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 (