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

• Published in: Acta mathematica scientia Vol. 35; no. 6; pp. 1349 - 1358
• Main Authors: BAHYRYCZ, Anna, CIEPLIŃSKI, Krzysztof, OLKO, Jolanta
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.11.2015; Institute of Mathematics, Pedagogical University, Podchor(az)ych 2, 30-084 Kraków, Poland%AGH University of Science and Technology, Faculty of Applied Mathematics,Mickiewicza 30, 30-059 Krakow, Poland
• Subjects: (generalized) Hyers-Ulam stability; 38B52; 39B72; 39B82; Cauchy's functional equation; fixed point method; Jensen's functional equation; multi-Cauchy-Jensen mapping; 函数方程; 定点法; 方程组; 映射; 柯西; 稳定性; multi-Cauchy-Jensen mapping; fixed point method; 38B52; (generalized) Hyers-Ulam stability; Cauchy's functional equation; Jensen's functional equation; 39B72; 39B82
• ISSN: 0252-9602; 1572-9087
• DOI: 10.1016/S0252-9602(15)30059-X

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.