Existence of solutions of polynomial-like iterative equation with discontinuous known functions

DOI10.1007/s11784-021-00871-3zbMath1472.39042OpenAlexW3192798444MaRDI QIDQ2045213

Jinghua Liu, Zhiheng Yu

Publication date: 12 August 2021

Published in: Journal of Fixed Point Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11784-021-00871-3

zbMATH Keywords

polynomial-like iterative equationBanach fixed point principlepiecewise bi-Lipschitz function

Mathematics Subject Classification ID

Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable (26A15) Fixed-point theorems (47H10) Iteration theory, iterative and composite equations (39B12) Rate of growth of functions, orders of infinity, slowly varying functions (26A12)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Convex solutions to polynomial-like iterative equations on open intervals
• Iterative equations in Banach spaces
• Mean-type mappings and invariant curves
• Convex solutions of polynomial-like iterative equations
• Construction of continuous solutions and stability for the polynomial-like iterative equation
• Decreasing solutions and convex solutions of the polynomial-like iterative equation
• Existence, uniqueness and stability of \(C^m\) solutions of iterative functional equations
• On the functional equation \(f(p+qx+rf(x))=a+bx+cf(x)\)
• Characteristic solutions of polynomial-like iterative equations
• On a linear iterative equation
• On an equation of linear iteration
• Invariant curves for a second-order difference equation modelled from macroeconomics
• Invariant Curves for Mappings
• When is f(f(z)) = az 2 + bz + c?
• Invariant curves for planar mappings
• Method of characteristic for functional equations in polynomial form
• Quadratic invariant curves for a planar mapping
• On Linear Dependence of Iterates
• Solutions of equivariance for a polynomial-like iterative equation
• Analytic invariant curves for a second order difference equation modelled from macroeconomics under the Brjuno condition
• Discussion on the differentiable solutions of the iterated equation
• Characteristic analysis for a polynomial-like iterative equation