The Fréchet functional equation with application to the stability of certain operators

DOI10.1016/j.jat.2011.09.009zbMath1238.39008OpenAlexW1997168156MaRDI QIDQ657439

Dorian Popa, Ioan Raşa

Publication date: 16 January 2012

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jat.2011.09.009

zbMATH Keywords

Fréchet functional equationBernstein-Schnabl operatorHyers-Ulam stability for linear operators

Mathematics Subject Classification ID

Functional equations for real functions (39B22) Stability, separation, extension, and related topics for functional equations (39B82) General (adjoints, conjugates, products, inverses, domains, ranges, etc.) (47A05) Generic properties, structural stability of dynamical systems (37C20)

Related Items (19)

Hyers-Ulam stability of differential operators on reproducing kernel function spaces ⋮ Hyperstability of general linear functional equation ⋮ On Hyers-Ulam stability of generalized linear functional equation and its induced Hyers-Ulam programming problem ⋮ A Bernstein-Schnabl type operator: Applications to difference equations ⋮ Hyperstability of some functional equations on restricted domain ⋮ On the generalized Fréchet functional equation with constant coefficients and its stability ⋮ \(C_{0}\)-semigroups of \(m\)-isometries on Hilbert spaces ⋮ On the stability of some classical operators from approximation theory ⋮ A functional definition of polynomial for connected Lie groups ⋮ Hyers-Ulam stability of differentiation operator on Hilbert spaces of entire functions ⋮ On some recent developments in Ulam's type stability ⋮ Power series method and approximate linear differential equations of second order ⋮ Steklov type operators and functional equations ⋮ On Ulam Stability of a Generalization of the Fréchet Functional Equation on a Restricted Domain ⋮ On Hyers-Ulam stability of fractional differential equations with Prabhakar derivatives ⋮ On the best constant in Hyers-Ulam stability of some positive linear operators ⋮ The Fréchet functional equation for Lie groups ⋮ Recursive procedure in the stability of Fréchet polynomials ⋮ On the stability of some positive linear operators from approximation theory

Cites Work

• On the Hyers-Ulam stability of the linear differential equation
• On the stability of the linear differential equation of higher order with constant coefficients
• Stability of a composite functional equation related to idempotent mappings
• On Bernstein-Schnabl operators on the unit interval
• Approximate solutions of the Gołąb-Schinzel equation
• On the asymptoticity aspect of Hyers-Ulam stability of mappings
• ESSENTIAL NORMS AND STABILITY CONSTANTS OF WEIGHTED COMPOSITION OPERATORS ON C(X)
• HYERS-ULAM STABILITY OF A CLOSED OPERATOR IN A HILBERT SPACE
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