A Variant of Jensen’s Inequalities (original) (raw)

An extension of Jensen's discrete inequality to half convex functions

Journal of Inequalities and Applications, 2011

We extend the right and left convex function theorems to weighted Jensen's type inequalities, and then combine the new theorems in a single one applicable to a half convex function f(u), defined on a real interval Á and convex for u ≤ s or u ≥ s, where s ∈ Á. The obtained results are applied for proving some open relevant inequalities.

Jensen-Type Inequalities for a Class of Convex Functions

2016

In this paper, we introduce a new class of function to obtain some interesting inequalities of Jensen- type. Our results generalize and refine some existing results in literature. Some applications for Schur's inequality are also included.

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.

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 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.

ON AN UPPER BOUND FOR JENSEN'S INEQUALITY

Journal of Inequalities in Pure and Applied Mathematics

In this paper we shall give another global upper bound for Jensen's discrete in- equality which is better than existing ones. For instance, we determine a new converse for the generalized A G inequality.

Continuous refinements of some Jensen-type inequalities via strong convexity with applications

Journal of Inequalities and Applications

In this paper we prove new continuous refinements of some Jensen type inequalities in both direct and reversed forms. As applications we also derive some continuous refinements of Hermite–Hadamard, Hölder, and Popoviciu type inequalities. As particular cases we point out the corresponding results for sums and integrals showing that our results contain both several well-known but also some new results for these special cases.

Several new cyclic Jensen type inequalities and their applications

Journal of Inequalities and Applications

We present some fundamental results and definitions regarding Jensen's inequality with the aim of obtaining new generalizations of cyclic refinements of Jensen's inequality from convex to higher order convex functions using Taylor's formula. We discuss the monotonicity of functionals for n-convex functions at a point. Applications of our work include new bounds for some important inequalities used in information theory.