A fixed point theorem in the space of integrable functions and applications

被引：0
作者：
G. J. de Cabral-García
K. Baquero-Mariaca
J. Villa-Morales
机构：
[1] Universidad Autónoma de Aguascalientes,Departamento de Matemáticas y Física
来源：
Rendiconti del Circolo Matematico di Palermo Series 2 | 2023年 / 72卷
关键词：
Fixed point theorem; Uniform integrability; Fredholm equations; Caputo fractional equations; Sequential compactness; Primary 47H10; Secondary 54C05;
D O I：
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学科分类号：
摘要：
We give sufficient conditions to ensure when a mapping T:E→E\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T:\varvec{E} \rightarrow \varvec{E}$$\end{document} has a unique fixed point, E is a set of measurable functions that is uniformly continuous, closed, and convex. The proof of the existence of the fixed point depends on a certain type of sequential compactness for uniformly integrable functions that is also studied. The fixed point theorem is applied in the study of the uniqueness and existence of some Fredholm and Caputo equations.
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页码：655 / 672
页数：17
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