A fixed point approach to stability of a quadratic equation

DOI10.1007/s00574-006-0016-zzbMath1118.39015arXivmath/0512007OpenAlexW2033656680MaRDI QIDQ854673

Mohammad Sal Moslehian, Madjid Mirzavaziri

Publication date: 6 December 2006

Published in: Bulletin of the Brazilian Mathematical Society. New Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0512007

zbMATH Keywords

Banach spaceadditive mappingorthogonality spaceorthogonal stabilityfixed point alternative theoremorthogonally additive mappingorthogonally quadratic mappingPexiderized quadratic functional equation

Mathematics Subject Classification ID

Stability, separation, extension, and related topics for functional equations (39B82) Functional equations for functions with more general domains and/or ranges (39B52) Orthogonal additivity and other conditional functional equations (39B55)

Related Items (97)

Non-Archimedean stability of a generalized reciprocal-quadratic functional equation in several variables by direct and fixed point methods ⋮ Fuzzy versions of Hyers-Ulam-Rassias theorem ⋮ On the quotient stability of a family of functional equations ⋮ Hyers-Ulam stability of an additive-quadratic functional equation ⋮ Random Stability of an AQCQ Functional Equation: A Fixed Point Approach ⋮ Fixed points and stability for functional equations in probabilistic metric and random normed spaces ⋮ A fixed point approach to the fuzzy stability of an additive-quadratic-cubic functional equation ⋮ A fixed point approach to the stability of an additive-quadratic-cubic-quartic functional equation ⋮ Stability of an AQCQ-functional equation in paranormed spaces ⋮ Fuzzy stability of functional inequalities in matrix fuzzy normed spaces ⋮ An AQCQ-functional equation in matrix Banach spaces ⋮ A fixed point theorem and the Hyers-Ulam stability in Riesz spaces ⋮ Functional Inequalities in Banach Spaces and Fuzzy Banach Spaces ⋮ Orthogonally Additive: Additive Functional Equation ⋮ Stability of a mixed functional equation in several variables on Banach modules ⋮ Lattictic non-Archimedean random stability of ACQ functional equation ⋮ On nonlinear stability in various random normed spaces ⋮ On stability of a functional equation of quadratic type ⋮ Orthogonal stability of an additive-quadratic functional equation ⋮ Stability of a generalized quadratic functional equation in various spaces: a fixed point alternative approach ⋮ Set-valued quadratic functional equations ⋮ A functional equation related to inner product spaces in non-Archimedean \(\mathcal L\)-random normed spaces ⋮ Unnamed Item ⋮ A fixed point approach to the stability of Pexider quadratic functional equation with involution ⋮ Measure zero stability problem of a generalized quadratic functional equation ⋮ Random homomorphisms and random derivations in random normed algebras via fixed point method ⋮ Approximation of linear mappings in Banach modules over \(C^\ast \)-algebras ⋮ Fixed point method for set-valued functional equations ⋮ Stability of an \(m\)th root functional equation in \(C^{*}\)-algebras: a fixed point approach ⋮ Orthogonal stability of functional equations with the fixed point alternative ⋮ Fuzzy -homomorphisms and fuzzy -derivations in induced fuzzy -algebras ⋮ A fixed point approach to the stability of an \(n\)-dimensional mixed-type additive and quadratic functional equation ⋮ Solution and stability of mixed type functional equation in non-Archimedean random normed spaces ⋮ A fixed point approach to stability of functional equations ⋮ Nonlinear random stability via fixed-point method ⋮ Set-Valued Additive Functional Equations ⋮ On the stability of an \(m\)-variables functional equation in random normed spaces via fixed point method ⋮ Fuzzy stability of a quadratic-additive functional equation ⋮ A fixed point approach to the stability of functional equations in non-Archimedean metric spaces ⋮ Unnamed Item ⋮ General solutions of two quadratic functional equations of Pexider type on orthogonal vectors ⋮ Approximation of functional equations in intuitionistic fuzzy C ∗ -algebras ⋮ Fuzzy approximation of Euler-Lagrange quadratic mappings ⋮ Fixed points, inner product spaces, and functional equations ⋮ Unnamed Item ⋮ On the generalized orthogonal stability of the pexiderized quadratic functional equations in modular spaces ⋮ Stability of functional equations in matrix random normed spaces: a fixed point approach ⋮ Generalized Ulam-Hyers stability of random homomorphisms in random normed algebras associated with the Cauchy functional equation ⋮ Hyperstability of the Cauchy equation on restricted domains ⋮ Generalized Hyers-Ulam stability of quadratic functional equations: a fixed point approach ⋮ On the stability of quadratic functional equations ⋮ A HYPERSTABILITY RESULT FOR THE CAUCHY EQUATION ⋮ On approximately of a \(\sigma\)-quadratic functional equation on a set of measure zero ⋮ Generalized stability of \(C^{\ast}\)-ternary quadratic mappings ⋮ Unnamed Item ⋮ Stability of functional inequalities in matrix random normed spaces ⋮ Stability of an AQCQ functional equation in non-Archimedean \((n, \beta)\)-normed spaces ⋮ C*-TERNARY HOMOMORPHISMS, C*-TERNARY DERIVATIONS, JB*-TRIPLE HOMOMORPHISMS AND JB*-TRIPLE DERIVATIONS ⋮ A fixed point method to the generalized stability of a mixed additive and quadratic functional equation in Banach modules ⋮ Fuzzy stability of additive functional inequalities with the fixed point alternative ⋮ Stability of homomorphisms and generalized derivations on Banach algebras ⋮ Fuzzy stability of an additive-quadratic-quartic functional equation ⋮ Random stability of an additive-quadratic-quartic functional equation ⋮ On the stability of the additive Cauchy functional equation in random normed spaces ⋮ Nonlinear \(\mathcal L\)-random stability of an ACQ functional equation ⋮ Fixed points and random stability of a generalized Apollonius type quadratic functional equation ⋮ Solutions and the generalized Hyers-Ulam-Rassias stability of a generalized quadratic-additive functional equation ⋮ On approximate additive-quartic and quadratic-cubic functional equations in two variables on Abelian groups ⋮ Stability of a cubic functional equation in intuitionistic random normed spaces ⋮ Generalized Hyers-Ulam stability of a mixed type functional equation ⋮ Fixed points and the stability of an AQCQ-functional equation in non-Archimedean normed spaces ⋮ Fixed points of a mapping and Hyers-Ulam stability ⋮ Stability of a Mixed Type Additive, Quadratic, Cubic and Quartic Functional Equation ⋮ Baire category theorem and approximation of the Pexider quadratic functional equation on a set of Lebesgue measure zero ⋮ STABILITY OF MAPPINGS ON MULTI-NORMED SPACES ⋮ Set-valued additive \(\rho \)-functional inequalities ⋮ Fixed points in functional inequalities ⋮ Fixed points and stability of a generalized quadratic functional equation ⋮ On approximation of approximately generalized quadratic functional equation via Lipschitz criteria ⋮ Functional equations in matrix normed spaces ⋮ FUZZY ALGEBRA HOMOMORPHISMS AND FUZZY DERIVATIONS ⋮ Unnamed Item ⋮ Asymptotic aspect of the quadratic functional equation in multi-normed spaces ⋮ On solution and stability of a two-variable functional equations ⋮ Stability of the Jensen-type functional equation in \(C^{\ast}\)-algebras: a fixed point approach ⋮ A fixed point approach to the stability of a quadratic functional equation in \(C^{\ast}\)-algebras ⋮ Approximate Euler-Lagrange quadratic mappings in fuzzy Banach spaces ⋮ Lipschitz stability of the k-quadratic functional equation ⋮ Fuzzy stability of the generalized version of drygas functional equation ⋮ Stability of functional equations in \((n,\beta)\)-normed spaces ⋮ Recent developments of the conditional stability of the homomorphism equation ⋮ Approximate solution of a generalized multi-quadratic type functional equation in Lipschitz spaces ⋮ ORTHOGONALLY ADDITIVE AND ORTHOGONALLY QUADRATIC FUNCTIONAL EQUATION ⋮ FUNCTIONAL EQUATIONS IN ORTHOGONALITY SPACES ⋮ STABILITY OF THE JENSEN FUNCTIONAL EQUATION IN FUZZY BANACH ALGEBRAS ⋮ Orthogonalities and functional equations ⋮ A fixed point theorem and Ulam stability of a general linear functional equation in random normed spaces

This page was built for publication: A fixed point approach to stability of a quadratic equation