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

共 50 条

[31] A NEW FIXED POINT THEOREM FOR CONE MAPS AND ITS APPLICATIONS [J].

Huang Chunchao (Fuzhou University) .

Annals of Differential Equations, 1998, (03) :498-505+56

[32] Some variants of Wardowski fixed point theorem [J].

Nazam, Muhammad ;

Aydi, Hassen ;

Park, Choonkil ;

Arshad, Muhammad ;

Savas, Ekrem ;

Shin, Dong Yun .

ADVANCES IN DIFFERENCE EQUATIONS, 2021, 2021 (01)

[33] A New Fixed Point Result and its Application to Existence Theorem for Nonconvex Hammerstein Type Integral Inclusions [J].

Pathak, Hemant Kumar ;

Shahzad, Naseer .

ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2012, (62) :1-13

[34] On a fixed point theorem of Kirk [J].

Arandelovic, ID .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2005, 301 (02) :384-385

[35] A strong fixed point theorem [J].

Pasicki, Lech .

TOPOLOGY AND ITS APPLICATIONS, 2020, 282

[36] ONE FIXED POINT THEOREM FOR MIXED MONOTONE OPERATORS AND APPLICATIONS TO NONLINEAR INTEGRAL EQUATIONS [J].

Wang, Haiying ;

Fang, Li .

JOURNAL OF INTEGRAL EQUATIONS AND APPLICATIONS, 2024, 36 (03) :371-382

[37] A Pata-type fixed point theorem in modular spaces with application [J].

Mohadeseh Paknazar ;

Madjid Eshaghi ;

Yeol Je Cho ;

Seyed Mansour Vaezpour .

Fixed Point Theory and Applications, 2013

[38] Some new extensions of Darbo's fixed point theorem with application [J].

Gencturk, Lker ;

Hancer, Hatice Aslan ;

Altun, Ishak .

FILOMAT, 2024, 38 (18) :6325-6332

[39] A Fixed Point Theorem and an Application for the Cauchy Problem in the Scale of Banach Spaces [J].

Vo Viet Tri ;

Karapinar, Erdal .

FILOMAT, 2020, 34 (13) :4387-4398

[40] An application of fixed point theorem to best approximation in locally convex space [J].

Nashine, Hemant Kumar ;

Khan, Mohammad Saeed .

APPLIED MATHEMATICS LETTERS, 2010, 23 (02) :121-127

← 1 2 3 4 5 →