A fixed point approach to the stability of functional equations in non-Archimedean metric spaces

被引：109
|
作者：
BrzdeK, Janusz [1 ]
Cieplinski, Krzysztof [1 ]
机构：
[1] Pedag Univ, Dept Math, PL-30084 Krakow, Poland
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2011年 / 74卷 / 18期
关键词：
Non-Archimedean normed space; Ultrametric; Fixed point; Hyers-Ulam stability; Functional equation in a single variable; Metric space; HYERS-ULAM STABILITY; ADDITIVE MAPPINGS; LINEAR RECURRENCE; NORMED SPACES; FIELDS;
D O I：
10.1016/j.na.2011.06.050
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this note, we prove a simple fixed point theorem for a special class of complete metric spaces (namely, complete non-Archimedean metric spaces which are connected with some problems coming from quantum physics, p-adic strings and superstrings). We also show that this theorem is a very efficient and convenient tool for proving the Hyers-Ulam stability of a quite wide class of functional equations in a single variable. (C) 2011 Elsevier Ltd. All rights reserved.
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页码：6861 / 6867
页数：7
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