Superstability of some Pexider-type functional equation
type: Item
instance of: scholarly article
title: Superstability of some Pexider-type functional equation
zbMATH Open document ID: 1214.39013
DOI: 10.1155/2010/985348
author: Gwang Hui Kim
published in: Journal of Inequalities and Applications
publication date: 2010-12-06T00:00:00Z
full work available at URL: https://eudml.org/doc/232487
review text: The author studies the superstability of the sine functional equation on the basis of the following Pexider-type functional equation \[ f(x+ y)+ g(x- y)= \lambda\cdot h(x)k(y), \] where \(k\) is a constant, which is actually a mixed functional equation. The problem studied in this paper has its origin in Ulam's problem for approximate homomorphism with its subsequent stability theorems of D. H. Hyers, T. Aoki, D. G. Bourgin, Th. M. Rassias and P. Găvruta. Reviewer's note: The following two books are useful treatises in the subject of the paper with several results and a number of applications of interdisciplinary character: {\parindent6.5mm \begin{itemize}\item[(1)] \textit{D. H. Hyers}, \textit{G. Isac} and \textit{Th. M. Rassias} [Stability of functional equations in several variables. Progress in Nonlinear Differential Equations and their Applications. 34. Boston, MA: Birkhäuser (1998; Zbl 0907.39025)]. \item[(2)] \textit{Pl. Kannappan} [Functional equations and inequalities with applications. Springer Monographs in Mathematics. New York, NY: Springer (2009; Zbl 1178.39032)]. \end{itemize}}
reviewed by: Themistocles M. Rassias
Mathematics Subject Classification ID: 39B82
Mathematics Subject Classification ID: 39B52
zbMATH DE Number: 5823211
zbMATH Keywords: superstability
zbMATH Keywords: Pexider-type functional equation
zbMATH Keywords: mixed functional equation
zbMATH Keywords: Banach spaces
zbMATH Keywords: unbounded Cauchy difference
zbMATH Keywords: sine functional equation
Wikidata QID: Q59252832
MaRDI profile type: Publication
OpenAlex ID: W2044211567
cites work: On the Stability of the Linear Functional Equation
cites work: Approximately isometric and multiplicative transformations on continuous function rings
cites work: On the stability of the linear transformation in Banach spaces
cites work: On the Stability of the Linear Mapping in Banach Spaces
cites work: On approximation of approximately linear mappings by linear mappings
cites work: The Stability of the Equation f(x + y) = f(x)f(y)
cites work: The Stability of the Cosine Equation
cites work: The superstability of d'Alembert's functional equation on the Heisenberg group
cites work: The stability of d'Alembert and Jensen type functional equations
cites work: On the superstability of the Pexider type trigonometric functional equation
cites work: The Stability of the Sine Equation
cites work: A stability of the generalized sine functional equations
cites work: On the stability of the generalized sine functional equations
cites work: Functional Equations and Inequalities with Applications
description: scientific article; zbMATH DE number 5823211