ON MULTI-JENSEN FUNCTIONS AND JENSEN DIFFERENCE

Title & Authors
ON MULTI-JENSEN FUNCTIONS AND JENSEN DIFFERENCE
Cieplinski, Krzysztof;

Abstract
In this paper we characterize multi-Jensen functions f : $\small{V^n\;{\rightarrow}\;W}$, where n is a positive integer, V, W are commutative groups and V is uniquely divisible by 2. Moreover, under the assumption that f : $\small{\mathbb{R}\;{\rightarrow}\;\mathbb{R}}$ is Borel measurable, we obtain representation of f (respectively, f, g, h : $\small{\mathbb{R}\;{\rightarrow}\;\mathbb{R}}$) such that the Jensen difference $\small{2f\;$$\frac{x\;+\;y}{2}$$\;-\;f(x)\;-\;f(y)}$ (respectively, the Pexider difference $\small{2f\;$$\frac{x\;+\;y}{2}$$\;-\;g(x)\;-\;h(y))}$ takes values in a countable subgroup of $\small{\mathbb{R}}$.
Keywords
Language
English
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