• Title/Summary/Keyword: multi-Jensen functions

Search Result 2, Processing Time 0.015 seconds

ON MULTI-JENSEN FUNCTIONS AND JENSEN DIFFERENCE

  • Cieplinski, Krzysztof
    • Bulletin of the Korean Mathematical Society
    • /
    • v.45 no.4
    • /
    • pp.729-737
    • /
    • 2008
  • 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 $\mathbb{R}$.

STABILITY OF THE MULTI-JENSEN EQUATION

  • Prager, Wolfgang;Schwaiger, Jens
    • Bulletin of the Korean Mathematical Society
    • /
    • v.45 no.1
    • /
    • pp.133-142
    • /
    • 2008
  • Given an $m{\in}\mathbb{N}$ and two vector spaces V and W, a function f : $V^m{\rightarrow}W$ is called multi-Jensen if it satisfies Jensen's equation in each variable separately. In this paper we unify these m Jensen equations to obtain a single functional equation for f and prove its stability in the sense of Hyers-Ulam, using the so-called direct method.