The properties of functional inclusions and Hyers-Ulam stability

DOI10.1007/s00010-012-0119-0zbMath1271.39031OpenAlexW2001280166MaRDI QIDQ1941999

Magdalena Piszczek

Publication date: 25 March 2013

Published in: Aequationes Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00010-012-0119-0

zbMATH Keywords

normed spaceHyers-Ulam stabilityselectionset-valued mapstability of functional equationfunctional inclusions

Mathematics Subject Classification ID

Set-valued maps in general topology (54C60) Selections in general topology (54C65) Stability, separation, extension, and related topics for functional equations (39B82) Functional equations for functions with more general domains and/or ranges (39B52) General theory of functional equations and inequalities (39B05)

Related Items (17)

Selections of generalized convex set-valued functions satisfying some inclusions ⋮ On selections of set-valued Euler-Lagrange inclusions with applications ⋮ On selections of set-valued inclusions in a single variable with applications to several variables ⋮ Remarks on hyperstability of the Cauchy functional equation ⋮ Unnamed Item ⋮ Fixed points of some nonlinear operators in spaces of multifunctions and the Ulam stability ⋮ Fixed point theory and the Ulam stability ⋮ On some recent developments in Ulam's type stability ⋮ On Selections of Some Generalized Set-Valued Inclusions ⋮ On selections of generalized convex set-valued maps ⋮ On convex-valued G-\(m\)-monomials with applications in stability theory ⋮ On the stability of additive, quadratic, cubic and quartic set-valued functional equations ⋮ Hyperstability and superstability ⋮ A note on stability of maps which preserve equality of distance ⋮ On Ulam's type stability of the linear equation and related issues ⋮ Ulam stability of some functional inclusions for multi-valued mappings ⋮ A note on stability of Fischer-Muszély functional equation

Cites Work

• Selections of set-valued maps satisfying a linear inclusion in a single variable
• Generalized stability of the Cauchy functional equation
• Comments on the core of the direct method for proving Hyers-Ulam stability of functional equations
• Hyers-Ulam stability of functional equations in several variables
• A Property of a Functional Inclusion Connected with Hyers-Ulam Stability
• On the Stability of the Linear Mapping in Banach Spaces
• Functional inclusions on square-symmetric grupoids and Hyers-Ulam stability
• On the Stability of the Linear Functional Equation
• Stability of functional equations in several variables
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