Jensen's Discrete Inequality Research Articles

An extension of Jensen’s discrete inequality to partially convex functions

This paper deals with a new extension of Jensen's discrete inequality to a partially convex function f , which is defined on a real interval I, convex on a subinterval (a, b) ⊂ I, decreasing for u ≤ c and increasing for u ≥ c ,w herec ∈ (a, b). Several relevant applications are given to show the effectiveness of the proposed partially convex function theorem. MSC: 26D07; 26D10; 41A44

The best lower bound for Jensen's inequality with three fixed ordered variables

In this paper we establish the best lower bound for the weighted Jensen's discrete inequality with ordered variables applied to a convex function f, in the case when the bound depends on f, weights and three xed variables. Some applications for particular cases of interest are provided.

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

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 and convex for u ≤ s or u ≥ s, where . The obtained results are applied for proving some open relevant inequalities.

Remarks on "On a Converse of Jensen's Discrete Inequality" of S. Simić

We show that the main results by S. Simic are special cases of results published many years earlier by J. E. Pecaric et al. (1992).

The Best Lower Bound Depended on Two Fixed Variables for Jensen's Inequality with Ordered Variables

We give the best lower bound for the weighted Jensen's discrete inequality with ordered variables applied to a convex function , in the case when the lower bound depends on , weights, and two given variables. Furthermore, under the same conditions, we give some sharp lower bounds for the weighted AM-GM inequality and AM-HM inequality.

On a new converse of Jensen's inequality

We give another global upper bound for Jensen's discrete inequality which is better than already existing ones. For instance, we determine a new converses for generalized A-G and G-H inequalities.

One refinement of Jensen's discrete inequality and applications

Jensen's inequality induces different forms of functionals which enables refinements for many classic inequalites. Several refinements of Jensen's inequalities were given. In this paper we refine Jensen's inequality by separating a discrete domain of it. At the end, we give some applications.

On a Converse of Jensen's Discrete Inequality

We give the best possible global bounds for a form of discrete Jensen's inequality. By some examples the fruitfulness of this result is shown.

The property of supermultiplicity for some classical inequalities and applications

In this paper, we shall discuss some new properties of supermultiplicity and logarithmic concavity for some mappings which are associated with Jensen's discrete inequality, Hölder's and Minkowski's inequalities, Čebyšev's inequality, and Cauchy-Buniakowski-Schwarz's inequality.

S-Orlicz Convex Functions in Linear Spaces and Jensen's Discrete Inequality

In this paper we consider the class ofs-Orlicz convex functions defined on as-Orlicz convex subset of a real linear space. Some inequalities of Jensen's type for this class of mappings are pointed out.

A counterpart of Jensen's discrete inequality for differentiable convex mappings and applications in information theory

We derive a counterpart of Jensen's discrete inequality for differentiable convex mappings defined on open subsets of R n . The result is applied to several convex functions. In particular, we obtain some meaningful bounds for entropy, conditional entropy, and mutual information arising from the theory of information.