Some Refinements Of Jensens Inequality On Product Spaces (original) (raw)

A Note on Some Variants of Jensen’s Inequality

2015

In this paper, we present a refined Steffensen’s inequality for convex functions and further prove some variants of Jensen’s inequality using the new Steffensen’s inequality. M. M. IDDRISU, C. A. OKPOTI and K. A. GBOLAGADE 64

A Note On Generalization Of Classical Jensens Inequality

The journal of mathematics and computer science, 2014

In this note, we prove a new generalisation of the Jensen's inequality by using a Riemann-Stieltjes integrable function and convex functions under a mild condition. An example was given to support the claims of this paper.

On Some Improvements of the Jensen Inequality with Some Applications

Journal of Inequalities and Applications, 2009

An improvement of the Jensen inequality for convex and monotone function is given as well as various applications for mean. Similar results for related inequalities of the Jensen type are also obtained. Also some applications of the Cauchy mean and the Jensen inequality are discussed.

A new version of Jensen’s inequality and related results

Journal of Inequalities and Applications, 2012

In this paper we expand Jensen's inequality to two-variable convex functions and find the lower bound of the Hermite-Hadamard inequality for a convex function on the bounded area from the plane.

On Some Refinements of Jensen's Inequality

Journal of Approximation Theory, 1998

This paper contains a link between Probability Proportional to Size (PPS) sampling and interpolations of the classical Jensen inequality. We show that these interpolating inequalities are, in fact, special cases of the conditional Jensen inequality when applied over an appropriate probability space. We provide a few examples dealing with divided differences, convex functions over linear spaces, approximation operators, and sampling with and without replacement.

Generalization and Refinements of Jensen Inequality

Journal of Mathematical Analysis, 2021

We give generalizations and refinements of Jensen and Jensen− Mercer inequalities by using weights which satisfy the conditions of Jensen and Jensen− Steffensen inequalities. We also give some refinements for discrete and integral version of generalized Jensen−Mercer inequality and shown to be an improvement of the upper bound for the Jensen’s difference given in [32]. Applications of our work include new bounds for some important inequalities used in information theory, and generalizing the relations among means.

On the refinements of the Jensen-Steffensen inequality

Journal of Inequalities and Applications, 2011

In this paper, we extend some old and give some new refinements of the Jensen-Steffensen inequality. Further, we investigate the log-convexity and the exponential convexity of functionals defined via 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. 2010 Mathematics Subject Classification. 26D15.

A Variant of Jensen’s Inequalities

In this paper, we give an estimate from below and from above of a variant of Jensen's Inequalities for convex functions in the discrete and continuous cases.