Construction of continuous solutions and stability for the polynomial-like iterative equation

DOI10.1016/J.JMAA.2006.02.065zbMath1111.39020OpenAlexW1966618470MaRDI QIDQ853992

Bing Xu, Wei Nian Zhang

Publication date: 7 December 2006

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.2006.02.065

zbMATH Keywords

continuityiterative rootiterative equationleading coefficientHyers--Ulam stability

Mathematics Subject Classification ID

Functional equations for real functions (39B22) Stability, separation, extension, and related topics for functional equations (39B82) Iteration theory, iterative and composite equations (39B12)

Related Items (31)

On a functional equation involving iterates and powers ⋮ Continuously decreasing solutions for a general iterative equation ⋮ Remarks on Stability of the Linear Functional Equation in Single Variable ⋮ Strongly convex solutions of a polynomial-like iterative equation with variable coefficients ⋮ Unbounded solutions of an iterative-difference equation ⋮ Strongly convex solutions of an iterative functional equation ⋮ Continuity of iteration and approximation of iterative roots ⋮ The \(C^0\) solutions of the Feigenbaum-like functional equation ⋮ Existence, construction and extension of continuous solutions of an iterative equation with multiplication ⋮ Global solutions for leading coefficient problem of polynomial-like iterative equations ⋮ Differentiable solutions of an equation with product of iterates ⋮ Convex solutions to polynomial-like iterative equations on open intervals ⋮ Iterative square roots of functions ⋮ On some recent developments in Ulam's type stability ⋮ On a Zoltán Boros' problem connected with polynomial-like iterative equations ⋮ The polynomial-like iterative equation for PM functions ⋮ Hyers-Ulam stability of an iterative equation for strictly increasing continuous functions ⋮ Local \(C^1\) stability versus global \(C^1\) unstability for iterative roots ⋮ Continuously decreasing solutions for polynomial-like iterative equations ⋮ Iterative roots of continuous functions and Hyers-Ulam stability ⋮ Global solutions for leading coefficient problem of a general iterative equation ⋮ Flatness, plateau limit and limit length of single-plateau functions ⋮ Leading coefficient problem for polynomial-like iterative equations ⋮ Continuous solutions of 3rd-order iterative equation of linear dependence ⋮ Strongly convex solutions of polynomial-like iterative equation ⋮ Construction of usc solutions for a multivalued iterative equation of order \(n\) ⋮ Existence of continuous solutions and stability for a general iterative functional equation ⋮ Stability for iterative roots of piecewise monotonic functions ⋮ Existence of solutions of polynomial-like iterative equation with discontinuous known functions ⋮ How violently do smooth iterative roots oscillate? ⋮ Local \(C^r\) stability for iterative roots of orientation-preserving self-mappings on the interval

Cites Work

• Iterative equations in Banach spaces
• Stability of functional equations in single variable.
• Existence, uniqueness and stability of \(C^m\) solutions of iterative functional equations
• On the functional equation \(f(p+qx+rf(x))=a+bx+cf(x)\)
• Iterative functional equations in the class of Lipschitz functions
• On existence for polynomial-like iterative equations
• Characteristic solutions of polynomial-like iterative equations
• On a linear iterative equation
• Hyers-Ulam stability of functional equations in several variables
• On an equation of linear iteration
• Iterative functional equation \(x(x(t))= f(t)\) with \(f(t)\) piecewise linear
• A functional equation involving iterates of a bijection on the unit interval II
• Continuous solutions of a polynomial-like iterative equation with variable coefficients
• Solutions of equivariance for a polynomial-like iterative equation
• Discussion on the differentiable solutions of the iterated equation
• Recent results on functional equations in a single variable, perspectives and open problems
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