Open Access Research

On the stability of set-valued functional equations with the fixed point alternative

Hassan A Kenary1, Hamid Rezaei1, Yousof Gheisari2 and Choonkil Park3*

Author Affiliations

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

2 Department of Mathematics, Islamic Azad University, Bushehr Branch, Bushehr, Iran

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

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Fixed Point Theory and Applications 2012, 2012:81 doi:10.1186/1687-1812-2012-81

Published: 10 May 2012

Abstract

Using the fixed point method, we prove the Hyers-Ulam stability of a Cauchy-Jensen type additive set-valued functional equation, a Jensen type additive-quadratic set-valued functional equation, a generalized quadratic set-valued functional equation and a Jensen type cubic set-valued functional equation.

Mathematics Subject Classification 2010: 47H10; 54C60; 39B52; 47H04; 91B44.

Keywords:
Hyers-Ulam stability; set-valued functional equation; fixed point