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APPROXIMATION OF CAUCHY ADDITIVE MAPPINGS

  • Roh, Jai-Ok (DEPARTMENT OF MATHEMATICS HALLYM UNIVERSITY) ;
  • Shin, Hui-Joung (DEPARTMENT OF MATHEMATICS CHUNGNAM NATIONAL UNIVERSITY)
  • Published : 2007.11.30

Abstract

In this paper, we prove that a function satisfying the following inequality $${\parallel}f(x)+2f(y)+2f(z){\parallel}{\leq}{\parallel}2f(\frac{x}{2}+y+z){\parallel}+{\epsilon}({\parallel}x{\parallel}^r{\cdot}{\parallel}y{\parallel}^r{\cdot}{\parallel}z{\parallel}^r)$$ for all x, y, z ${\in}$ X and for $\epsilon{\geq}0$, is Cauchy additive. Moreover, we will investigate for the stability in Banach spaces.

Keywords

Hyers-Ulam stability;Cauchy additive mapping;Jordan-von Neumann type Cauchy Jensen functional equation

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