Remarks on hyperstability of the Cauchy functional equation
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Publication:387614
DOI10.1007/s00010-012-0168-4zbMath1303.39016OpenAlexW2108584017MaRDI QIDQ387614
Publication date: 23 December 2013
Published in: Aequationes Mathematicae (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00010-012-0168-4
normed spaceHyers-Ulam stabilitycocycleCauchy functional equationhyperstabilityconditional functional equation
Stability, separation, extension, and related topics for functional equations (39B82) Orthogonal additivity and other conditional functional equations (39B55)
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Cites Work
- Stability of multi-additive mappings in \(\beta\)-Banach spaces
- Applications of fixed point theorems to the Hyers-Ulam stability of functional equations -- a survey
- Hyers-Ulam-Rassias stability of functional equations in nonlinear analysis
- On the stability of functional equations
- A note on stability of the general linear equation
- On orthogonally additive mappings
- On a modified Hyers-Ulam sequence
- On stability of additive mappings
- On a generalization of the Cauchy functional equation
- A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings
- On the generalized Hyers-Ulam stability of module left \((m,n)\)-derivations
- The properties of functional inclusions and Hyers-Ulam stability
- Extensions of certain homomorphisms of subsemigroups to homomorphisms of groups
- Generalized Cauchy difference functional equations
- Approximately isometric and multiplicative transformations on continuous function rings
- On the stability of the linear transformation in Banach spaces
- Generalized Cauchy difference equations. II
- Christensen Zero Sets and Measurable Convex Functions
- On the Stability of the Linear Mapping in Banach Spaces
- On almost additive functions
- Some Functional Equations in Groups and Rings.
- On the Stability of the Linear Functional Equation
- Stability of functional equations in several variables
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