A fixed point approach to the stability of a general mixed AQCQ-functional equation in non-Archimedean normed spaces
type: Item
instance of: scholarly article
title: A fixed point approach to the stability of a general mixed AQCQ-functional equation in non-Archimedean normed spaces
zbMATH Open document ID: 1198.39041
DOI: 10.1155/2010/812545
published in: Discrete Dynamics in Nature and Society
publication date: 2010-09-29T00:00:00Z
full work available at URL: https://eudml.org/doc/231277
review text: Summary: Using fixed point methods, we prove the generalized Hyers-Ulam stability of the general mixed additive-quadratic-cubic-quartic functional equation \[ \begin{multlined} f(x+ky)+f(x - ky)=k^{2}f(x+y)+k^{2}f(x - y)+2(1 - k^{2})f(x)\\ +\frac{k^4 - k^2}{12}[f(2y)+f( - 2y) - 4f(y) - 4f( - y)]\end{multlined} \] for a fixed integer \(k\) with \(k\neq 0,\pm \)1 in non-Archimedean normed spaces.
Mathematics Subject Classification ID: 39B82
Mathematics Subject Classification ID: 39B52
zbMATH DE Number: 5793508
zbMATH Keywords: generalized Hyers-Ulam stability
zbMATH Keywords: general mixed additive-quadratic-cubic-quartic (AQCQ) functional equation
zbMATH Keywords: non-Archimedean normed spaces
author: Tian Zhou Xu
author: J. M. Rassias
author: Wan Xin Xu
MaRDI profile type: Publication
OpenAlex ID: W2061839786
Wikidata QID: Q58650649
cites work: Q3259049
cites work: On the Stability of the Linear Functional Equation
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: A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings
cites work: Solution of a problem of Ulam
cites work: Q4950687
cites work: On approximation of approximately linear mappings by linear mappings
cites work: Q5460093
cites work: Q3654660
cites work: Generalized Hyers-Ulam stability of a general mixed additive-cubic functional equation in quasi-Banach spaces
cites work: Intuitionistic fuzzy stability of a general mixed additive-cubic equation
cites work: Solution of the Ulam stability problem for cubic mappings
cites work: Functional inequalities in non-Archimedean Banach spaces
cites work: Stability of a mixed type cubic-quartic functional equation in non-Archimedean spaces
cites work: Q4211216
cites work: On the stability of the additive Cauchy functional equation in random normed spaces
cites work: APPROXIMATELY ADDITIVE MAPPINGS IN NON-ARCHIMEDEAN NORMED SPACES
cites work: Stability of functional equations in non-Archimedean spaces
cites work: A Mazur--Ulam theorem in non-Archimedean normed spaces
cites work: Stability of two types of cubic functional equations in non-archimedean spaces
cites work: Q3633110
cites work: Some remarks on stability and solvability of linear functional equations
cites work: Fixed points and the stability of an AQCQ-functional equation in non-Archimedean normed spaces
cites work: A note to paper ``On the stability of cubic mappings and quartic mappings in random normed spaces''
cites work: A generalized mixed quadratic-quartic functional equation
cites work: Q4492826
cites work: Q5283909
cites work: Stability of \(\Psi\)-additive mappings: Applications to nonlinear analysis
cites work: Q4470094
cites work: A fixed point theorem of the alternative, for contractions on a generalized complete metric space
description: scientific article; zbMATH DE number 5793508