Fuzzy stability of a functional equation associated with inner product spaces
type: Item
instance of: scholarly article
title: Fuzzy stability of a functional equation associated with inner product spaces
zbMATH Open document ID: 1182.39023
author: Choonkil Park
published in: Fuzzy Sets and Systems
publication date: 2009-11-17T00:00:00Z
review text: Using some ideas of \textit{A. K. Mirmostafaee} and \textit{M. S. Moslehian} [Fuzzy Sets Syst. 159, No.~6, 720--729 (2008; Zbl 1178.46075)], the author proves the generalized Hyers-Ulam stability of the functional equation \[ 2f\left(\frac{x+y}{2}\right)+f\left(\frac{x-y}{2}\right)+f\left(\frac{y-x}{2}\right)=f(x)+f(y) \] in fuzzy Banach spaces for odd and even cases. This functional equation is related to a characterization of inner product spaces; see \textit{M. S. Moslehian} [Linear Algebra Appl. 429, No.~8--9, 2159--2167 (2008; Zbl 1156.47021)].
reviewed by: Mohammad Sal Moslehian
Mathematics Subject Classification ID: 39B82
Mathematics Subject Classification ID: 39B72
Mathematics Subject Classification ID: 46S40
Mathematics Subject Classification ID: 26E50
Mathematics Subject Classification ID: 46S50
Mathematics Subject Classification ID: 39B52
Mathematics Subject Classification ID: 46C05
zbMATH DE Number: 5634462
zbMATH Keywords: fuzzy Banach space
zbMATH Keywords: functional equation
zbMATH Keywords: generalized Hyers-Ulam stability
zbMATH Keywords: inner product space
MaRDI profile type: Publication
full work available at URL: j.fss.2008.11.027
OpenAlex ID: W1995581110
cites work: On the stability of the linear transformation in Banach spaces
cites work: Q4458997
cites work: Fuzzy bounded linear operators
cites work: Q4846621
cites work: Remarks on the stability of functional equations
cites work: On the stability of the quadratic mapping in normed spaces
cites work: Finite dimensional fuzzy normed linear space
cites work: A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings
cites work: On the Stability of the Linear Functional Equation
cites work: Hyers-Ulam-Rassias stability of functional equations in mathematical analysis
cites work: Fuzzy topological vector spaces. II
cites work: Separation of fuzzy normed linear spaces
cites work: Fuzzy stability of the Jensen functional equation
cites work: Fuzzy versions of Hyers-Ulam-Rassias theorem
cites work: On the stability of the linear mapping in Banach modules
cites work: Modified Trif's functional equations in Banach modules over a \(C\)-algebra and approximate algebra homomorphisms.
cites work: On an approximate automorphism on a $C^{*}$-algebra
cites work: Lie \(\ast\)-homomorphisms between Lie \(C^*\)-algebras and Lie \(\ast\)-derivations on Lie \(C^*\)-algebras
cites work: Homomorphisms between Poisson JC*-algebras
cites work: AN APPLICATION OF THE LERAY-SCHAUDER DEGREE THEORY TO THE VARIABLE COEFFICIENT SEMILINEAR BIHARMONIC PROBLEM
cites work: On the Stability of the Linear Mapping in Banach Spaces
cites work: Q3333552
cites work: Q4791365
cites work: The problem of S. M. Ulam for approximately multiplicative mappings
cites work: On the stability of functional equations in Banach spaces
cites work: On the stability of functional equations and a problem of Ulam
cites work: On the Behavior of Mappings which do not Satisfy Hyers-Ulam Stability
cites work: On the Hyers-Ulam stability of linear mappings
cites work: Variational problem of some quadratic functionals in complex analysis
cites work: Proprieta’ locali e approssimazione di operatori
cites work: Q3259049
cites work: Fuzzy normed space of operators and its completeness
DOI: 10.1016/J.FSS.2008.11.027
description: scientific article; zbMATH DE number 5634462