Result: A GENERALIZATION OF THE HYERS-ULAM-RASSIAS STABILITY OF A FUNCTIONAL EQUATION OF DAVISON: A generalization of the Hyers-Ulam-Rassias stability of a functional equation of Davison
Title:
A GENERALIZATION OF THE HYERS-ULAM-RASSIAS STABILITY OF A FUNCTIONAL EQUATION OF DAVISON: A generalization of the Hyers-Ulam-Rassias stability of a functional equation of Davison
Authors:
Source:
Journal of the Korean Mathematical Society. 41:501-511
Publisher Information:
The Korean Mathematical Society, 2004.
Publication Year:
2004
Subject Terms:
Document Type:
Academic journal
Article
File Description:
application/xml
Language:
English
ISSN:
0304-9914
DOI:
10.4134/jkms.2004.41.3.501
Access URL:
Accession Number:
edsair.doi.dedup.....da2a4b0cac617b3a2e24f193bf6bf55f
Database:
OpenAIRE
Further Information
The functional equation \(f(xy)+f(x+y)=f(xy+x)+f(y)\) was introduced by \textit{T. M. K. Davison} [Problem 191R1. Aequationes Math. 20, 306 (1980)]. Its general solution was recently given by \textit{R. Girgensohn} and \textit{K. Lajkó} [ibid. 60, No.~3, 219--224 (2000; Zbl 0970.39017)]. The stability of this equation was investigated by \textit{S.-M. Jung} and \textit{P. K. Sahoo} [J. Math. Anal. Appl. 238, No.~1, 297--304 (1999; Zbl 0933.39052); Kyungpook Math. J. 40, No.~1, 87--92 (2000; Zbl 0967.39010)]. Let \(F\) be a ring with the unit element, let~\(E\) be a~Banach space and let \(\varphi:F\times F\to[0,\infty)\) satisfies the condition \(\sum_{n=1}^{\infty}2^{-n}\varphi(2^{n-1}x,2^{n-1}y+z)