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http://dx.doi.org/10.4134/BKMS.2008.45.4.729

ON MULTI-JENSEN FUNCTIONS AND JENSEN DIFFERENCE  

Cieplinski, Krzysztof (INSTITUTE OF MATHEMATICS PEDAGOGICAL UNIVERSITY)
Publication Information
Bulletin of the Korean Mathematical Society / v.45, no.4, 2008 , pp. 729-737 More about this Journal
Abstract
In this paper we characterize multi-Jensen functions f : $V^n\;{\rightarrow}\;W$, where n is a positive integer, V, W are commutative groups and V is uniquely divisible by 2. Moreover, under the assumption that f : $\mathbb{R}\;{\rightarrow}\;\mathbb{R}$ is Borel measurable, we obtain representation of f (respectively, f, g, h : $\mathbb{R}\;{\rightarrow}\;\mathbb{R}$) such that the Jensen difference $$2f\;\(\frac{x\;+\;y}{2}\)\;-\;f(x)\;-\;f(y)$$ (respectively, the Pexider difference $$2f\;\(\frac{x\;+\;y}{2}\)\;-\;g(x)\;-\;h(y))$$ takes values in a countable subgroup of $\mathbb{R}$.
Keywords
multi-Jensen function; multi-additive mapping; stability; Jensen difference; Pexider difference;
Citations & Related Records
Times Cited By KSCI : 4  (Citation Analysis)
Times Cited By Web Of Science : 6  (Related Records In Web of Science)
Times Cited By SCOPUS : 10
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