STABILITY OF MAPPINGS ON MULTI-NORMED SPACES

DOI10.1017/S0017089507003552zbMath1125.39023OpenAlexW2110245212MaRDI QIDQ5757158

Mohammad Sal Moslehian, H. Garth Dales

Publication date: 6 September 2007

Published in: Glasgow Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0017089507003552

zbMATH Keywords

fixed pointsHyers-Ulam stabilityCauchy functional equationmulti-Banach spacemulti-normed spaceRassias stabilitymulti-normGăvruta stabilityunique multi-bounded linear mapping

Mathematics Subject Classification ID

Stability, separation, extension, and related topics for functional equations (39B82) Geometry and structure of normed linear spaces (46B20) Functional equations for functions with more general domains and/or ranges (39B52)

Related Items (27)

Multi-\(C^{*}\)-ternary algebras and applications ⋮ Approximation of involution in multi-Banach algebras: fixed point technique ⋮ On the stability of alternative additive equations in multi-\(\beta\)-normed spaces ⋮ Orthogonal stability of mixed type additive-cubic functional equations in multi-Banach spaces ⋮ Stability and nonstability of octadecic functional equation in multi-normed spaces ⋮ Mean ergodic theorem for semigroups of linear operators in multi-Banach spaces ⋮ A Fixed Point Approach to Stability of the Quadratic Equation ⋮ Approximation of a generalized additive mapping in multi-Banach modules and isomorphisms in multi-\(C^\ast\)-algebras: a fixed-point approach ⋮ Power-norms based on Hilbert \(C^\ast\)-modules ⋮ General Solution and Hyers–Ulam Stability of DuoTrigintic Functional Equation in Multi-Banach Spaces ⋮ Stability of an additive-cubic-quartic functional equation in multi-Banach spaces ⋮ Approximations of ternary Jordan homomorphisms and derivations in multi-\(C^*\) ternary algebras ⋮ A fixed points approach to stability of the Pexider equation ⋮ Remarks on the Cauchy functional equation and variations of it ⋮ On the stability of the additive Cauchy functional equation in random normed spaces ⋮ The mean ergodic theorem for nonexpansive mappings in multi-Banach spaces ⋮ Stability of a mixed type functional equation on multi-Banach spaces: a fixed point approach ⋮ Ψ-Aditive Mappings and Hyers–Ulam Stability ⋮ A fixed point method for stability of involutions on multi-Banach algebra ⋮ Asymptotic aspect of the quadratic functional equation in multi-normed spaces ⋮ Application of the product net technique and Kadec-Klee property to study nonlinear ergodic theorems and weak convergence theorems in uniformly convex multi-Banach spaces ⋮ Unnamed Item ⋮ On the Generalized Hyers–Ulam Stability of the Pexider Equation on Restricted Domains ⋮ Multi-generalized 2-normed space ⋮ Unnamed Item ⋮ Stability of trigintic functional equation in multi-Banach spaces: fixed point approach ⋮ A fixed point theorem and Ulam stability of a general linear functional equation in random normed spaces

Cites Work

• A fixed point approach to stability of a quadratic equation
• Approximate homomorphisms of ternary semigroups
• On stability of additive mappings
• A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings
• Stability of \(\Psi\)-additive mappings: Applications to nonlinear analysis
• Approximately vanishing of topological cohomology groups
• On the stability of \(J^*\)-homomorphisms
• Approximately Multiplicative Functionals
• Approximately Multiplicative Maps Between Banach Algebras
• On the Behavior of Mappings which do not Satisfy Hyers-Ulam Stability
• On the Stability of the Linear Mapping in Banach Spaces
• On the Stability of the Linear Functional Equation

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