ON AN EQUATION CHARACTERIZING MULTI-CAUCHY-JENSEN MAPPINGS AND ITS HYERS-ULAM STABILITY

doi:10.1016/S0252-9602(15)30059-X

Abstract

Abstract:

In this paper, we give two characterizations of multi-Cauchy-Jensen mappings. One of them reduces the system of n equations defining these mappings to a single functional equation. We also prove, using the fixed point method, the generalized Hyers-Ulam stability of this equation. Our results generalize some known outcomes.

Key words: multi-Cauchy-Jensen mapping, (generalized) Hyers-Ulam stability, Cauchy's functional equation, Jensen's functional equation, fixed point method

CLC Number:

39B82

Anna BAHYRYCZ, Krzysztof CIEPLINSKI, Jolanta OLKO. ON AN EQUATION CHARACTERIZING MULTI-CAUCHY-JENSEN MAPPINGS AND ITS HYERS-ULAM STABILITY[J].Acta mathematica scientia,Series B, 2015, 35(6): 1349-1358.

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