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Stability of a pexiderial functional equation in random normed spaces

  • Hassan Azadi KenaryEmail author
Article

Abstract

The concept of Hyers-Ulam-Rassias stability originated from Th.M. Rassias’ stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72:297–300, 1978. Recently, the generalized Hyers-Ulam-Rassias stability of the following quadratic functional equation
$$f(x+y)+f(x-y)=2f(x)+2f(y)$$
proved in the earlier work. In this paper, using direct method we prove the generalized Hyers-Ulam stability of the following Pexiderial functional equation
$$f(x+y)+f(x-y)=2g(x)+2g(y)$$
in random normed space.

Keywords

Hyers-Ulam stability Random normed spaces 

Mathematics Subject Classification (2000)

39B22 39B52 

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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Department of Mathematics, College of SciencesYasouj UniversityYasoujIran

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