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.
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
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
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