Approximation of an additive mapping in various normed spaces

Document Type: Research Paper

Authors

1 Department of Mathematics‎, ‎Arsanjan Branch‎, ‎Islamic Azad University‎, ‎Arsanjan‎, ‎Iran.

2 Department of Mathematics‎, ‎College of Sciences‎, ‎Yasouj University‎, ‎Yasouj 75918-74831‎, ‎Iran.

Abstract

In this paper, using the fixed point and direct methods, we prove the generalized Hyers-Ulam-Rassias stability
of the following Cauchy-Jensen additive functional equation:
begin{equation}label{main}
fleft(frac{x+y+z}{2}right)+fleft(frac{x-y+z}{2}right)=f(x)+f(z)end{equation}
in various normed spaces.
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 (1978), 297-300.

Keywords

Main Subjects



Volume 41, Issue 5
September and October 2015
Pages 1213-1233
  • Receive Date: 25 January 2014
  • Revise Date: 22 July 2014
  • Accept Date: 22 July 2014