On the stability of set-valued functional equations with the fixed point alternative

DOI10.1186/1687-1812-2012-81zbMath1283.39010OpenAlexW2123568359WikidataQ59289639 ScholiaQ59289639MaRDI QIDQ372091

Hamid Rezaei, Yousof Gheisari, Hassan Azadi Kenary, Chun-Gil Park

Publication date: 11 October 2013

Published in: Fixed Point Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/1687-1812-2012-81

zbMATH Keywords

generalized metric spaceUlam-Hyers stabilityalternative fixed pointCauchy set-valued functional equationquadratic set-valued functional equation

Mathematics Subject Classification ID

Set-valued maps in general topology (54C60) Fixed-point and coincidence theorems (topological aspects) (54H25) Stability, separation, extension, and related topics for functional equations (39B82) Functional equations for functions with more general domains and/or ranges (39B52)

Related Items (12)

On a cyclic Jungck modified \(TS\)-iterative procedure with application examples ⋮ Stability of two types of cubic fuzzy set-valued functional equations ⋮ Unnamed Item ⋮ Hyers-Ulam-Rassias stability of some additive fuzzy set-valued functional equations with the fixed point alternative ⋮ Some properties of distances and best proximity points of cyclic proximal contractions in metric spaces ⋮ A new approach to Hyers-Ulam stability of \(r\)-variable quadratic functional equations ⋮ On the stability of additive, quadratic, cubic and quartic set-valued functional equations ⋮ On the Ulam type stability of several types of quadratic fuzzy set-valued functional equations ⋮ On the stability of fuzzy set-valued functional equations ⋮ On the stability of the generalized Cauchy-Jensen set-valued functional equations ⋮ On the stability of the generalized cubic set-valued functional equation ⋮ On the new Hyers–Ulam–Rassias stability of the generalized cubic set-valued mapping in the incomplete normed spaces

Cites Work

• Unnamed Item
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• Unnamed Item
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• Unnamed Item
• Lattictic non-Archimedean random stability of ACQ functional equation
• Local stability of the pexiderized Cauchy and Jensen's equations in fuzzy spaces
• A fixed point approach to the Hyers-Ulam stability of a functional equation in various normed spaces
• Stability of the Jensen equation in \(C^*\)-algebras: a fixed point approach
• Solution and Hyers-Ulam-Rassias stability of generalized mixed type additive-quadratic functional equations in fuzzy Banach spaces
• Generalized Hyers-Ulam stability of the Pexiderized Cauchy functional equation in non-archimedean spaces
• On approximate \(C^*\)-ternary \(m\)-homomorphisms: a fixed point approach
• Selections of set-valued maps satisfying a linear inclusion in a single variable
• The stability of the quartic functional equation in various spaces
• Stability of mixed additive-quadratic Jensen type functional equation in various spaces
• Generalized Hyers-Ulam stability of quadratic functional equations: a fixed point approach
• Fixed point methods for the generalized stability of functional equations in a single variable
• Random stability of an additive-quadratic-quartic functional equation
• Approximately \(J^*\)-homomorphisms: a fixed point approach
• Stability of a mixed type cubic-quartic functional equation in non-Archimedean spaces
• Fuzzy stability of a functional equation associated with inner product spaces
• Convex analysis and measurable multifunctions
• A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings
• On the stability of functional equations and a problem of Ulam
• On the Hyers-Ulam stability of \(\psi\)-additive mappings
• Birkhoff integral for multi-valued functions
• Stability of \(\Psi\)-additive mappings: Applications to nonlinear analysis
• Fixed points and stability for quadratic mappings in \(\beta\)-normed left Banach modules on Banach algebras
• The fixed point method for fuzzy approximation of a functional equation associated with inner product spaces
• On the stability of \(J^*\)-derivations
• Fixed points and Hyers--Ulam--Rassias stability of Cauchy--Jensen functional equations in Banach algebras
• Integrals of set-valued functions
• On the stability of the linear transformation in Banach spaces
• Some results on stability and on characterization of K-convexity of set-valued functions
• On the Existence of General Equilibrium for a Competitive Market
• Proprieta’ locali e approssimazione di operatori
• On the Stability of the Linear Mapping in Banach Spaces
• A fixed point method for perturbation of bimultipliers and Jordan bimultipliers in C∗-ternary algebras
• Stability of homomorphisms on JB^✻-triples associated to a Cauchy-Jensen type functional equation
• A fixed point theorem of the alternative, for contractions on a generalized complete metric space
• Existence of an Equilibrium for a Competitive Economy
• On the Stability of the Linear Functional Equation
• Remarks on the stability of functional equations
• Set-valued analysis
• Stability of functional equations in several variables
• On the stability of the quadratic mapping in normed spaces

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