Existence, uniqueness and stability of \(C^m\) solutions of iterative functional equations

DOI10.1007/BF02879796zbMath0999.39020MaRDI QIDQ1609567

Jie Hua Mai, Xin-He Liu

Publication date: 15 August 2002

Published in: Science in China. Series A (Search for Journal in Brave)

zbMATH Keywords

stabilityfixed pointiterative functional equationfunction spacecompact convex setdiagonal method\(C^m\) map

Mathematics Subject Classification ID

Stability, separation, extension, and related topics for functional equations (39B82) Iteration theory, iterative and composite equations (39B12)

Related Items

Continuously decreasing solutions for a general iterative equation, Construction of continuous solutions and stability for the polynomial-like iterative equation, Decreasing solutions and convex solutions of the polynomial-like iterative equation, Convex solutions of the multi-valued iterative equation of order \(n\), Global solutions for leading coefficient problem of polynomial-like iterative equations, On set-valued solution of an \(n\)-order iterative functional equation, The polynomial-like iterative equation for PM functions, Analytic solutions of systems of functional equations., Continuously decreasing solutions for polynomial-like iterative equations, Leading coefficient problem for polynomial-like iterative equations, Analytic Solutions of aq-Difference Equation and Applications to Iterative Equations^*, Construction of usc solutions for a multivalued iterative equation of order \(n\), Analytic solutions of iterative functional equations, Existence of continuous solutions and stability for a general iterative functional equation, A general class of iterative equations on the unit circle, Differentiable solutions of equations involving iterated functional series, Existence of solutions of polynomial-like iterative equation with discontinuous known functions, On series-like iterative equation with a general boundary restriction

Cites Work

• On a functional equation involving iterates of a bijection on the unit interval
• When is f(f(z)) = az 2 + bz + c?
• Fractional iteration of differentiable functions
• Discussion on the differentiable solutions of the iterated equation
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