Approximate additive mappings in 2-Banach spaces and related topics

DOI10.1016/j.jmaa.2010.10.004zbMath1213.39028OpenAlexW2066264125MaRDI QIDQ624570

Won-Gil Park

Publication date: 9 February 2011

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

Full work available at URL: https://doi.org/10.1016/j.jmaa.2010.10.004

zbMATH Keywords

quadratic mappingUlam-Hyers stabilityadditive mapping2-Banach spacesJensen mappinglinear \(2\)-normed spaces

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 (48)

Ulam stability and non-stability of additive functional equation in IFN-spaces and 2-Banach spaces by different methods ⋮ Stability of Cauchy-Jensen Type Functional Equation in (2, α)–Banach Spaces ⋮ A new fixed point theorem in quasi-\((2, \beta)\)-Banach spaces and some of its applications to functional equations ⋮ Hyers-Ulam stability and hyperstability of a Jensen-type functional equation on 2-Banach spaces ⋮ Hyperstability criterion for a new type of 2-variable radical functional equations ⋮ Unnamed Item ⋮ On a fixed point theorem in 2-Banach spaces and some of its applications ⋮ Approximate mixed type quadratic-cubic functional equation ⋮ Some hyperstability results of a p-radical functional equation related to quartic mappings in non-archimedean Banach spaces ⋮ Approximate solution of \(p\)-radical functional equation in 2-Banach spaces ⋮ On a cubic-quadratic equation relative to elliptic curves ⋮ More on Hyers' theorem ⋮ On the Brzdȩk's fixed point approach to stability of a Drygas functional equation in 2-Banach spaces ⋮ Unnamed Item ⋮ Fixed points and approximately octic mappings in non-Archimedean 2-normed spaces ⋮ Unnamed Item ⋮ Approximation of two general functional equations in 2-Banach spaces ⋮ Nearly radical quadratic functional equations in \(p-2\)-normed spaces ⋮ On the Hyers-Ulam stability of a general mixed additive and cubic functional equation in \(n\)-Banach spaces ⋮ Equivalence for various forms of quadratic functional equations and their generalized Hyers-Ulam-Rassias stability ⋮ Approximate multi-variable bi-Jensen-type mappings ⋮ On Stability of the Functional Equation of p-Wright Affine Functions in 2-Banach Spaces ⋮ Approximation of radical functional equations related to quadratic and quartic mappings ⋮ A general system of Euler-Lagrange-type quadratic functional equations in Menger probabilistic non-Archimedean 2-normed spaces ⋮ Unnamed Item ⋮ Approximation of general \(\alpha\)-cubic functional equations in 2-Banach spaces ⋮ Prešić type results in 2-Banach spaces ⋮ Hyers-Ulam stability of quadratic forms in 2-normed spaces ⋮ Additive functional inequalities in 2-Banach spaces ⋮ On a functional equation connected with bi-linear mappings and its Hyers-Ulam stability ⋮ Approximate solution of radical quartic functional equation related to additive mapping in 2-Banach spaces ⋮ Unnamed Item ⋮ Approximate solutions of a quadratic functional equation in 2-Banach spaces using fixed point theorem ⋮ APPROXIMATE ADDITIVE MAPPINGS IN 2-BANACH SPACES AND RELATED TOPICS: REVISITED ⋮ THE GENERALIZED HYERS-ULAM STABILITY OF ADDITIVE FUNCTIONAL INEQUALITIES IN NON-ARCHIMEDEAN 2-NORMED SPACE ⋮ On the Hyers-Ulam stabilities of functional equations on n-Banach spaces ⋮ ON APPROXIMATELY ADDITIVE MAPPINGS IN 2-BANACH SPACES ⋮ Approximate solution of generalized inhomogeneous radical quadratic functional equations in 2-Banach spaces ⋮ Approximate multi-Jensen, multi-Euler-Lagrange additive and quadratic mappings in \(n\)-Banach spaces ⋮ On some inequalities in 2-metric spaces ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Approximate generalized Jensen mappings in 2-Banach spaces ⋮ Some hyperstability results in non-Archimedean 2-Banach space for a \(\sigma\)-Jensen functional equation ⋮ Stability of various functional equations in non-Archimedean \((n,\beta)\)-normed spaces ⋮ On stability of the functional equation of \(p\)-Wright affine functions in \((2,\alpha)\)-Banach spaces ⋮ Stability of functional equations in \((n,\beta)\)-normed spaces ⋮ Stability of a general p-radical functional equation related to additive mappings in 2-Banach spaces

Cites Work

• Unnamed Item
• Unnamed Item
• On a general Hyers-Ulam stability result
• On the stability of the linear transformation in Banach spaces
• Proprieta’ locali e approssimazione di operatori
• Lineare 2‐normierte Räume
• 2‐Banach Spaces
• Über 2‐BANACH‐Räume
• 2‐metrische Räume und ihre topologische Struktur
• On the Stability of the Linear Functional Equation

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