ON NEW APPROXIMATIONS FOR GENERALIZED CAUCHY FUNCTIONAL EQUATIONS USING BRZDȨK AND CIEPLIŃSKI'S FIXED POINT THEOREMS IN 2-BANACH SPACES  

作　　者：Laddawan AIEMSOMBOON Wutiphol SINTUNAVARAT 

机构地区：[1]Department of Mathematics and Statistics,Faculty of Science and Technology,Thammasat University Rangsit Center,Pathumthani 12121,Thailand

出　　处：《Acta Mathematica Scientia》2020年第3期824-834,共11页数学物理学报（B辑英文版）

基　　金：This work was supported by Research Professional Development Project under the Science Achievement Scholarship of Thailand(SAST)and Thammasat University Research Fund,Contract No.TUGG 33/2562;The second author would like to thank the Thailand Research Fund and Office of the Higher Education Commission under grant no.MRG6180283 for financial support during the preparation of this manuscript.

摘　　要：In this work,we apply the Brzdȩk and Ciepliński's fixed point theorem to investigate new stability results for the generalized Cauchy functional equation of the form f(ax+by)=af(x)+bf(y),where a,b∈N and f is a mapping from a commutative group(G,+)to a 2-Banach space(Y,||·,·||).Our results are generalizations of main results of Brzdȩk and Ciepliński[J Brzdȩk,K Ciepliński.On a fixed point theorem in 2-normed spaces and some of its applications.Acta Mathematica Scientia,2018,38B(2):377-390].

关 键 词：Fixed point theorem generalized Cauchy functional equation 2-normed space stability 

分 类 号：O177.2[理学—数学]