*-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

A Review of Hermite-Hadamard Inequality

Zenodo (CERN European Organization for Nuclear Research), 2022

In this review we present the most important lines of development, around the wellknown Hermite-Hadamard Inequality, as well as some open problems.

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 (

Some results on Hermite-Hadamard inequalities

2020

In this paper, we establish Hermite-Hadamard inequalities for uniformly p-convex functions and uniformly q-convex functions. Also, we obtain some new inequalities of Hermite-Hadamard type for functions whose derivatives in absolute value are the class of uniformly p-convex.

Some new inequalities of Hermite-Hadamard's type

Kyungpook Mathematical Journal, 2010

In this paper, we establish several new inequalities for some differantiable mappings that are connected with the celebrated Hermite-Hadamard integral inequality. Some applications for special means of real numbers are also provided.

On the generalized Hermite-Hadamard inequalities

Annals of the University of Craiova - Mathematics and Computer Science Series, 2020

In this paper, we present a new definition which generalizes some significant well known fractional integral operators such as Riemann-Liouville fractional integral, k-Riemann-Liouville fractional integral, Katugampola fractional operators, conformable fractional integral, Hadamard fractional integrals, etc. Then, using a general class of this generalized fractional integral operator, we establish new generalized fractional integral inequalities of Hermite-Hadamard type which cover the previously published results.

New Hermite–Hadamard Type Inequalities Involving Non-Conformable Integral Operators

Symmetry

At present, inequalities have reached an outstanding theoretical and applied development and they are the methodological base of many mathematical processes. In particular, Hermite– Hadamard inequality has received considerable attention. In this paper, we prove some new results related to Hermite–Hadamard inequality via symmetric non-conformable integral operators.

On the Hermite-Hadamard type inequalities

Journal of Inequalities and Applications, 2013

In the present paper, we establish some new Hermite-Hadamard type inequalities involving two functions. Our results in a special case yield recent results on Hermite-Hadamard type inequalities. MSC: 26D15

The Hermite-Hadamard Type Inequalities for Operator Godunova-Levin Class of Functions in Hilbert Space

Ordu üniversitesi bilim ve teknoloji dergisi, 2016

In this paper, firstly we defined a new operator function class in Hilbert Space for Hermite-Hadamard type inequalities via Godunova-Levin functions, i.e., we introduce class. Secondly, we established some new theorems for them. Finally, we obtained The Hermite-Hadamard type inequalities for the product two operators Godunova-Levin functions in Hilbert Space.

On the generalized inequalities of the Hermite-Hadamard type

Filomat, 2021

In this paper, we establish new Hermite-Hadamard inequalities for h-convex functions, with in the framework of a previously defined generalized integral. The results obtained, generalize or complete, several reported in the literature. Some final remarks show the strength and scope of our results.

Some generalized Hermite–Hadamard–Fejér inequality for convex functions

Advances in Difference Equations

In this paper, we have established some generalized inequalities of Hermite–Hadamard–Fejér type for generalized integrals. The results obtained are applied for fractional integrals of various type and therefore contain some previous results reported in the literature.