Continuous dependence of fixed points on parameters, remetrization theorems, and an application to the initial value problem

DOI10.1002/mma.8852OpenAlexW4308448200MaRDI QIDQ6147235

Jacek R. Jachymski

Publication date: 15 January 2024

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mma.8852

zbMATH Keywords

contractioninitial value problemcomplete metric spaceNemytskiĭ operatorremetrizationcontinuous dependence of fixed points

Mathematics Subject Classification ID

Complete metric spaces (54E50) Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) Particular nonlinear operators (superposition, Hammerstein, Nemytski?, Uryson, etc.) (47H30) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09)

Cites Work

• Sequences of contractions and fixed points
• Sequences of contractive maps and fixed points
• The Hutchinson-Barnsley theory for infinite iterated function systems
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