Open Access Research

Random homomorphisms and random derivations in random normed algebras via fixed point method

Choonkil Park1, Madjid Eshaghi Gordji2 and Reza Saadati3*

Author Affiliations

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

2 Department of Mathematics, Semnan University, P.O. Box 35195-363, Semnan, Iran

3 Department of Mathematics, Iran University of Science and Technology, Tehran, Iran

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Journal of Inequalities and Applications 2012, 2012:194 doi:10.1186/1029-242X-2012-194

Published: 4 September 2012

Abstract

Using the fixed point method, we prove the Hyers-Ulam stability of the Cauchy additive functional inequality and of the Cauchy-Jensen additive functional inequality in random normed spaces.

MSC: 47H10, 39B52, 37H10, 60H25, 17B40, 39B72, 47B47, 54E70.

Keywords:
additive functional inequality; fixed point; random derivation; random homomorphism; Hyers-Ulam stability; random normed algebra