Title : ( On linear functional equations and completeness of normed spaces )
Authors: A. Fosner , R. Ger , A. Gilanyi , Mohammad Sal Moslehian ,
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Abstract
The aim of this note is to give a type of characterization of Banach spaces in terms of the stability of functional equations. More precisely, we prove that a normed space X is complete if there exists a functional equation of the type sum_{i=1}^{n}a_if( vph_i(x_1, ldots,x_k))=0 qquad(x_1, ldots,x_k in D) with given real numbers a_1, ldots,a_n$, given mappings vph_1 ldots, vph_n colon D^k to D and unknown function f colon D to X , which has a Hyers--Ulam stability property on an infinite subset D of the integers.
Keywords
, Hyers--Ulam stability, normed space, completeness, Banach space
@article{paperid:1037804,
author = {A. Fosner and R. Ger and A. Gilanyi and Sal Moslehian, Mohammad},
title = {On linear functional equations and completeness of normed spaces},
journal = {Banach Journal of Mathematical Analysis},
year = {2013},
volume = {7},
number = {1},
month = {June},
issn = {1735-8787},
pages = {196--200},
numpages = {4},
keywords = {Hyers--Ulam stability; normed space; completeness; Banach space},
}
%0 Journal Article
%T On linear functional equations and completeness of normed spaces
%A A. Fosner
%A R. Ger
%A A. Gilanyi
%A Sal Moslehian, Mohammad
%J Banach Journal of Mathematical Analysis
%@ 1735-8787
%D 2013
