Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2016; 53(2): 387-398

Printed March 31, 2016

https://doi.org/10.4134/BKMS.2016.53.2.387

Copyright © The Korean Mathematical Society.

On a composite functional equation related to the Golab-Schinzel equation

Madjid Eshaghi Gordji, Themistocles M. Rassias, Mohamed Tial, and Driss Zeglami

Islamic Azad University, National Technical University of Athens, IBN Tofail University, E.N.S.A.M, Moulay Ismail University

Abstract

Let $X$ be a vector space over a field $K$ of real or complex numbers and $ k\in \mathbb{N}$. We prove the superstability of the following generalized Golab--Schinzel type equation \begin{equation*} f(x_{1}+\sum_{i=2}^{p}x_{i}f(x_{1})^{k} f(x_{2})^{k}\cdots f(x_{i-1})^{k})=\prod \limits_{i=1}^{p}f(x_{i}),\ x_{1},x_{2},\ldots,x_{p}\in X, \end{equation*} where $f:X\rightarrow K$ is an unknown function which is hemicontinuous at the origin.

Keywords: Hyers-Ulam stability, Golab--Schinzel equation, superstability

MSC numbers: Primary 39B72, 39B22, 39B32