Approximation of Cauchy additive mappings
Bull. Korean Math. Soc. 2007 Vol. 44, No. 4, 851-860
Published online December 1, 2007
Jaiok Roh and Hui Joung Shin
Hallym University, Chungnam National University
Abstract : In this paper, we prove that a function satisfying the following inequality $$ {\parallel f(x) + 2f(y)+ 2f(z)\parallel} \le {\parallel 2 f(\frac{x}{2}+y+z)\parallel} + \epsilon ({\parallel x\parallel}^r \cdot {\parallel y\parallel}^r \cdot {\parallel z\parallel}^r) $$ for all $x, y, z \in X$ and for $\epsilon \ge 0$, 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
MSC numbers : Primary: 39B52, 39B62, 39B72
Downloads: Full-text PDF  


Copyright © Korean Mathematical Society. All Rights Reserved.
The Korea Science Technology Center (Rm. 411), 22, Teheran-ro 7-gil, Gangnam-gu, Seoul 06130, Korea
Tel: 82-2-565-0361  | Fax: 82-2-565-0364  | E-mail: paper@kms.or.kr   | Powered by INFOrang Co., Ltd