On the stability of functional equations in Banach spaces

DOI10.1006/jmaa.2000.7046zbMath0964.39026OpenAlexW2077944191MaRDI QIDQ1589960

Themistocles M. Rassias

Publication date: 11 July 2001

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jmaa.2000.7046

zbMATH Keywords

Banach spacequadratic functional equationgeneralized Hyers-Ulam stabilityadditive functional equationd'Alembert equationtrigonometric functional equationsexponential 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)

Related Items (only showing first 100 items - show all)

Multi-\(C^{*}\)-ternary algebras and applications ⋮ A fixed point result and the stability problem in Lie superalgebras ⋮ Isometric isomorphisms in proper \(CQ^*\)-algebras ⋮ On the Drygas functional equation in restricted domains ⋮ Functional equations in paranormed spaces ⋮ Non-Archimedean Hyers-Ulam-Rassias stability of m-variable functional equation ⋮ Stability of an AQCQ-functional equation in paranormed spaces ⋮ Fuzzy \(\ast\)-homomorphisms and fuzzy \(\ast\)-derivations in induced fuzzy \(C^\ast\)-algebras ⋮ Stability of a quadratic Jensen type functional equation in the spaces of generalized functions ⋮ Approximately additive Schwartz distributions ⋮ On generalized Hyers-Ulam stability of additive mapings on restricted domains of Banach spaces ⋮ On the stability of an \(n\)-dimensional cubic functional equation ⋮ On the stability problem for a mixed type of quartic and quadratic functional equation ⋮ Isomorphisms between \(C^{*}\)-ternary algebras ⋮ On the stability of an AQCQ-functional equation in random normed spaces ⋮ Approximate \((m,n)\)-Cauchy-Jensen additive mappings in \(C^\ast\)-algebras ⋮ Orthogonality and quintic functional equations ⋮ Lattictic non-Archimedean random stability of ACQ functional equation ⋮ Local stability of the pexiderized Cauchy and Jensen's equations in fuzzy spaces ⋮ Orthogonal stability of an additive-quadratic functional equation ⋮ On the stability of trigonometric functional equations in distributions and hyperfunctions ⋮ Fuzzy Hyers-Ulam approximation of a mixed AQ mapping ⋮ Approximate Euler-Lagrange quadratic mappings ⋮ Almost partial generalized Jordan derivations: a fixed point approach ⋮ Orthogonally additive-additive and orthogonally quadratic-quadratic functional equation in orthogonality spaces ⋮ Approximate homomorphisms and derivations on random Banach algebras ⋮ Stability of approximately quadratic Schwartz distributions ⋮ Stability problems of quintic mappings in quasi-\(\beta \)-normed spaces ⋮ Solutions and stability of generalized mixed type QC functional equations in random normed spaces ⋮ Approximately intertwining mappings ⋮ Stability problem for Jensen-type functional equations of cubic mappings ⋮ Cauchy-Rassias stability of Cauchy-Jensen additive mappings in Banach spaces ⋮ The \(N\)-isometric isomorphisms in linear \(N\)-normed \(C^{\ast}\)-algebras ⋮ On the stability of Euler-Lagrange type cubic mappings in quasi-Banach spaces ⋮ Generalized stabilities of two functional equations ⋮ Hyers-Ulam stability of polynomial equations ⋮ Hyers-Ulam stability of functional equations in matrix normed spaces ⋮ Fixed points and stability of functional equations in fuzzy ternary Banach algebras ⋮ Fixed point theory and the Ulam stability ⋮ Fuzzy -homomorphisms and fuzzy -derivations in induced fuzzy -algebras ⋮ Stability of functional equations on restricted domains in a group and their asymptotic behaviors ⋮ Approximately quadratic mappings on restricted domains ⋮ Approximate \(n\)-Lie homomorphisms and Jordan \(n\)-Lie homomorphisms on \(n\)-Lie algebras ⋮ On a generalized Hyers-Ulam stability of trigonometric functional equations ⋮ On the stability of an \(m\)-variables functional equation in random normed spaces via fixed point method ⋮ General cubic-quartic functional equation ⋮ Non-Archimedean stability of a quadratic functional equation ⋮ Ulam-Hyers-Rassias stability problem for several kinds of mappings ⋮ Stability of an additive-cubic-quartic functional equation in multi-Banach spaces ⋮ Stability of a mixed additive and cubic functional equation in several variables in non-Archimedean spaces ⋮ Functional inequalities associated with Cauchy additive functional equation in non-Archimedean spaces ⋮ Stability of a pexiderial functional equation in random normed spaces ⋮ A fixed point method for almost partial derivations of Jensen type \(n\)-variable functional equations ⋮ Generalized Hyers-Ulam stability of quadratic functional equations: a fixed point approach ⋮ Stability of the Cauchy-Jensen functional equation in \(C^*\)-algebras: a fixed point approach ⋮ On the stability of a new Pexider-type functional equation ⋮ On the stability of generalized additive functional inequalities in Banach spaces ⋮ On Hyers-Ulam-Rassias stability of functional equations ⋮ Stability problem of Hyers-Ulam-Rassias for generalized forms of cubic functional equation ⋮ Stability of the Cauchy additive functional equation on tangle space and applications ⋮ Fixed points and stability of an additive functional equation of \(n\)-Apollonius type in \(C^{\ast}\)-algebras ⋮ Stability of exponential equations in Schwartz distributions ⋮ On the stability of a cubic functional equation ⋮ Functional equation \(f(x)=pf(x - 1) - qf(x - 2)\) and its Hyers-Ulam stability ⋮ Fuzzy stability of additive functional inequalities with the fixed point alternative ⋮ Quadratic-quartic functional equations in RN-spaces ⋮ On the stability of generalized quartic mappings in quasi-\(\beta\)-normed spaces ⋮ Fuzzy stability of an additive-quadratic-quartic functional equation ⋮ Random stability of an additive-quadratic-quartic functional equation ⋮ Stability of trigonometric functional equations in generalized functions ⋮ Stability of an additive-cubic-quartic functional equation ⋮ The stability of a quadratic functional equation with the fixed point alternative ⋮ On a generalized nonlinear functional equation ⋮ On the asymptoticity aspect of Hyers-Ulam stability of quadratic mappings ⋮ Nonlinear \(\mathcal L\)-random stability of an ACQ functional equation ⋮ Generalized Hyers-Ulam stability of the Pexiderized Cauchy functional equation in non-archimedean spaces ⋮ Hyers-Ulam stability of additive set-valued functional equations ⋮ Stability of the pexiderized Cauchy and Jensen's equations on restricted domains ⋮ The stability of Cauchy's gamma-beta functional equation ⋮ On the Hyers-Ulam-Rassias stability of functional equations in \(n\)-variables ⋮ Approximate quartic and quadratic mappings in quasi-Banach spaces ⋮ Generalized Hyers-Ulam-Rassias stability of \(n\)-sesquilinear-quadratic mappings on Banach modules over \(C^*\)-algebras ⋮ Isomorphisms between unital \(C^{\ast}\)-algebras ⋮ Fuzzy stability of quadratic functional equations ⋮ Fixed points and the stability of an AQCQ-functional equation in non-Archimedean normed spaces ⋮ Set-valued additive \(\rho \)-functional inequalities ⋮ A new hyperstability result for the Apollonius equation on a restricted domain and some applications ⋮ Functional inequalities in non-Archimedean Banach spaces ⋮ A note on stability of maps which preserve equality of distance ⋮ Fixed points in functional inequalities ⋮ Jordan *-derivations on \(C^*\)-algebras and \(JC^*\)-algebras ⋮ Stability of a functional equation deriving from cubic and quartic functions ⋮ Functional equations in matrix normed spaces ⋮ Approximately quintic and sextic mappings form \(r\)-divisible groups into Šerstnev probabilistic Banach spaces: fixed point method ⋮ Fixed points and stability of the Cauchy functional equation in \(C^{\ast }\)-algebras ⋮ Homomorphisms and derivations in \(C^{\ast}\)-ternary algebras ⋮ 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 ⋮ Stability of a generalized Euler-Lagrange type additive mapping and homomorphisms in \(C^{\ast}\)-algebras ⋮ Solution and stability of a mixed type additive, quadratic, and cubic functional equation

Cites Work

• Perturbations of Banach algebras
• Quasi-additive functions
• The stability of homomorphisms and amenability, with applications to functional equations
• On functions behaving like additive functions
• On stability of the Cauchy equation on semigroups
• On the stability of gamma functional equation
• On approximation of approximately linear mappings by linear mappings
• On a modified Hyers-Ulam sequence
• On stability of additive mappings
• On the Hyers-Ulam stability of the functional equations that have the quadratic property
• Remark on the stability of the gamma functional equation
• The functional equation of multiplicative derivation is superstable on standard operator algebras
• A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings
• On the Hyers-Ulam-Rassias stability of approximately additive mappings
• On the superstability of the functional equation \(f(x^ y)=yf(x)\)
• On a modified Hyers-Ulam stability of homogeneous equation
• On the stability of functional equations and a problem of Ulam
• On the stability of a system of functional equations characterizing generalized hyperbolic and trigonometric functions
• On the Hyers-Ulam stability of \(\psi\)-additive mappings
• On a general Hyers-Ulam stability result
• On Hyers-Ulam stability of Hosszú's functional equation
• On the stability of some functional equations for generalized hyperbolic functions and for the generalized cosine equation
• Hyers-Ulam stability of functional equations in several variables
• On the stability of Hosszú's functional equation
• On the stability of the quadratic functional equation on bounded domains
• On the Hyers-Ulam stability of linear mappings
• On an asymptotic behavior of exponential functional equation
• Approximately Multiplicative Functionals
• The Stability of the Sine Equation
• On a Local Stability of the Jensen Functional Equation
• Proprieta’ locali e approssimazione di operatori
• Approximately Multiplicative Maps Between Banach Algebras
• The Stability of the Cosine Equation
• On a Theorem of Baker, Lawrence and Zorzitto
• On the Behavior of Mappings which do not Satisfy Hyers-Ulam Stability
• The Stability of the Equation f(x + y) = f(x)f(y)
• On the Stability of the Linear Mapping in Banach Spaces
• Hyers-Ulam-Rassias stability of Jensen’s equation and its application
• On the asymptoticity aspect of Hyers-Ulam stability of mappings
• Note on a Stability Theorem
• The stability of the exponential equation
• The Stability of the Sine and Cosine Functional Equations
• On the Stability of the Linear Functional Equation
• Remarks on the stability of functional equations
• Approximate homomorphisms
• On the stability of the quadratic mapping in normed spaces
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: On the stability of functional equations in Banach spaces