A LOCAL FIXED POINT THEOREM AND ITS APPLICATION TO LINEAR OPERATORS

被引：0

作者：

Wardowski, Dariusz ^{[1
]}

机构：

[1] Univ Lodz, Fac Math & Comp Sci, Dept Nonlinear Anal, Banacha 22, PL-90238 Lodz, Poland

来源：

JOURNAL OF NONLINEAR AND CONVEX ANALYSIS | 2019年 / 20卷 / 10期

关键词：

(tau; F)-contraction; fixed point; homeomorphism; invertible linear operator;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the article, first we prove a local version of a fixed point theorem concerning the mapping T satisfying the following condition of F-contractive type: for all u, v in an open ball of the Banach space parallel to T(u) - T(v) parallel to <= parallel to u-v parallel to / 1 + tau parallel to u - v parallel to, where tau > 0. Next, for this type of mapping T defined on a non-empty open subset of the Banach space, we prove that the mapping I-T is a homeomorphism. Finally, the results obtained are applied in order to show that some linear operators defined on a Banach space are invertible.

引用

页码：2217 / 2223

页数：7

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