Open Access Research

A fixed point approach to the hyers-ulam stability of a functional equation in various normed spaces

Hassan A Kenary1, Sun Y Jang2 and Choonkil Park3*

Author Affiliations

1 Department of Mathematics, College of Sciences, Yasouj University, Yasouj 75914-353, Iran

2 Department of Mathematics, University of Ulsan, Ulsan 680-749, Korea

3 Department of Mathematics, Research Institute for Natural Sciences, Hanyang University, Seoul 133-791, Korea

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Fixed Point Theory and Applications 2011, 2011:67 doi:10.1186/1687-1812-2011-67

Published: 25 October 2011

Abstract

Using direct method, Kenary (Acta Universitatis Apulensis, to appear) proved the Hyers-Ulam stability of the following functional equation

<a onClick="popup('http://www.fixedpointtheoryandapplications.com/content/2011/1/67/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.fixedpointtheoryandapplications.com/content/2011/1/67/mathml/M1">View MathML</a>

in non-Archimedean normed spaces and in random normed spaces, where m, n are different integers greater than 1. In this article, using fixed point method, we prove the Hyers-Ulam stability of the above functional equation in various normed spaces.

2010 Mathematics Subject Classification: 39B52; 47H10; 47S40; 46S40; 30G06; 26E30; 46S10; 37H10; 47H40.

Keywords:
Hyers-Ulam stability; non-Archimedean normed space; random normed space; fuzzy normed space; fixed point method