On some fixed-point theorems for generalized contractions and their perturbations

被引：9

作者：

Borkowski, Marcin ^{[1
]}

Bugajewski, Dariusz ^{[2
]}

Zima, Miroslawa ^{[3
]}

机构：

[1] Adam Mickiewicz Univ Poznan, Fac Math & Comp Sci, Optimizat & Control Theory Dept, PL-61614 Poznan, Poland

[2] Morgan State Univ, Baltimore, MD 21251 USA

[3] Univ Rzeszow, Inst Math, PL-35310 Rzeszow, Poland

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2010年 / 367卷 / 02期

关键词：

Absolute retract; Banach space with a quasimodulus; Cone; Contractive mapping; Functional-integral equations; Hyperconvex metric space; Increasing multifunction; Krasnoselskii-type fixed-point theorems; Non-Archimedean normed space; Nonexpansive mapping; Nonlinear alternative; Palais-Smale condition; Schaefer-type fixed-point theorem; Spectral radius; Spherical completeness; Weakly contractive mapping; Weakly expanding mapping; SPACES; EQUATIONS;

D O I：

10.1016/j.jmaa.2010.01.014

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The aim of this paper is to prove a collection of fixed-point theorems for mappings which can be roughly called generalized contractions or their perturbations. In particular, we are going to consider operators (single-valued or multi-valued) in Banach spaces with a quasimodulus, in hyperconvex subsets of normed spaces, or finally in non-Archimedean spaces. A particular attention will be paid to Krasnoselskii-type fixed-point theorems as well as to a Schaefer-type fixed-point theorem. Some applications to nonlinear functional-integral equations will be given. Our results extend and complement some commonly known theorems. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：464 / 475

页数：12

共 28 条

[21] SOLVABILITY OF NONLINEAR VOLTERRA AND FREDHOLM EQUATIONS IN WEIGHTED SPACES [J].

NIETO, JJ ;

XU, HK .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1995, 24 (08) :1289-1297

[22] A FIXED-POINT THEOREM IN NON-ARCHIMEDEAN VECTOR-SPACES [J].

PETALAS, C ;

VIDALIS, T .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1993, 118 (03) :819-821

[23]

SCHAEFER H., 1960, Pacific J. Math., V10, P1009

[24]

Schauder J.P., 1930, Studia Math., V2, P171, DOI [10.4064/sm-2-1-171-180, DOI 10.4064/SM-2-1-171-180]

[25]

Sine R. C., 1979, Nonlinear Analysis Theory, Methods & Applications, V3, P885, DOI 10.1016/0362-546X(79)90055-5

[26] EXISTENCE OF FIXED-POINTS OF NONEXPANSIVE MAPPINGS IN CERTAIN BANACH-LATTICES [J].

SOARDI, PM .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1979, 73 (01) :25-29

[27]

Zeidler E, 1993, NONLINEAR FUNCTIONAL

[28] A CERTAIN FIXED-POINT THEOREM AND ITS APPLICATIONS TO INTEGRAL-FUNCTIONAL EQUATIONS [J].

ZIMA, M .

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 1992, 46 (02) :179-186

← 1 2 3 →