On the stability of pexider functional equation in non-archimedean spaces

Reza Saadati,Seiyed Mansour Vaezpour,Zahra Sadeghi

doi:10.1186/1029-242x-2011-17

Abstract

In this paper, the Hyers-Ulam stability of the Pexider functional equation in a non-Archimedean space is investigated, where σ is an involution in the domain of the given mapping f.MSC 2010:26E30, 39B52, 39B72, 46S10

Highlights

The stability problem for functional equations first was planed in 1940 by Ulam [1]: Let G1 be group and G2 be a metric group with the metric d(·,·)
The result of Hyers was generalized by Aoki [3] for additive mappings and Rassias [4] for linear mappings by considering an unbounded Cauchy difference
The paper of Rassias [4] has provided a lot of influences in the development of the Hyers-Ulam-Rassias stability of functional equations

Summary

Introduction

The stability problem for functional equations first was planed in 1940 by Ulam [1]: Let G1 be group and G2 be a metric group with the metric d(·,·). The function | · | : K ® R is called a non-Archimedean valuation or absolute value over the field K if it satisfies following conditions: for any a, b Î K, (1) |a| ≥ 0; (2) |a| = 0 if and only if a = 0; (3) |ab| = |a| |b| (4) |a + b| ≤ max{|a|, |b|}; (5) there exists a member a0 Î K such that |a0| ≠ 0, 1.

Results

Conclusion