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].
Laddawan AIEMSOMBOON
,
Wutiphol SINTUNAVARAT
. ON NEW APPROXIMATIONS FOR GENERALIZED CAUCHY FUNCTIONAL EQUATIONS USING BRZDȨK AND CIEPLIŃSKI'S FIXED POINT THEOREMS IN 2-BANACH SPACES[J]. Acta mathematica scientia, Series B, 2020
, 40(3)
: 824
-834
.
DOI: 10.1007/s10473-020-0316-1
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