Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

Article

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Commun. Korean Math. Soc. 2013; 28(2): 319-333

Printed April 1, 2013

https://doi.org/10.4134/CKMS.2013.28.2.319

Copyright © The Korean Mathematical Society.

Approximate Euler-Lagrange-Jensen type additive mapping in multi-Banach spaces: A fixed point approach

Fridoun Moradlou

Sahand University of Technology

Abstract

Using the fixed point method, we prove the generalized Hyers-Ulam-Rassias stability of the following functional equation in multi-\linebreak Banach spaces: \begin{equation*} \sum_{1 \le i < j \le n}f\Big(\frac{r_ix_i +r_jx_j}{k}\Big) = \frac{n-1}{k}\sum_{i=1}^{n}r_if(x_i). \end{equation*}

Keywords: fixed point method, Hyers--Ulam--Rassias stability, multi-Banach spaces, Euler-Lagrange mapping