Open Access Research

Hyers-Ulam-Rassias stability of the additive-quadratic mappings in non-Archimedean Banach spaces

C Park1, H Azadi Kenary2* and TM Rassias3

Author Affiliations

1 Department of Mathematics, Hanyang University, Seoul, South Korea

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

3 Department of Mathematics, National Technical University of Athens, Zografou, Campus, Athens, 15780, Greece

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Journal of Inequalities and Applications 2012, 2012:174 doi:10.1186/1029-242X-2012-174

Published: 6 August 2012

Abstract

Using the fixed point and direct methods, we prove the generalized Hyers-Ulam stability of the following additive-quadratic functional equation in non-Archimedean normed spaces

<a onClick="popup('http://www.journalofinequalitiesandapplications.com/content/2012/1/174/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.journalofinequalitiesandapplications.com/content/2012/1/174/mathml/M1">View MathML</a>

where r, s, γ are positive real numbers.

MSC: 39B55, 46S10.

Keywords:
Hyers-Ulam stability; fixed point method; non-Archimedean normed spaces