Fixed point theory for cyclic φ-contractions

被引：167

作者：

Pacurar, Madalina ^{[1
]}

Rus, Ioan A. ^{[2
]}

机构：

[1] Univ Babes Bolyai, Fac Econ & Business Adm, Cluj Napoca 400591, Romania

[2] Univ Babes Bolyai, Fac Math & Comp Sci, Cluj Napoca 400084, Romania

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2010年 / 72卷 / 3-4期

关键词：

Cyclic phi-contraction; Picard operator; Data dependence; Well-posedness of the fixed point problem; Limit shadowing property;

D O I：

10.1016/j.na.2009.08.002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Following [W.A. Kirk, P.S. Srinivasan, P. Veeramany, Fixed points for mappings satisfying cyclical contractive conditions, Fixed Point Theory 4 (1) (2003) 79-89], we present a fixed point theorem for cyclic phi-contractions and following [I.A Rus, The theory of a metrical fixed point theorem: Theoretical and applicative relevances, Fixed Point Theory 9 (2) (2008) 541-559] we construct a theory of this fixed point theorem. This theory is in connection with data dependence, well-posedness of the fixed point problem, limit shadowing property and sequences of operators and fixed points. A Maia type fixed point theorem for cyclic phi-contractions is also given. (C) 2009 Elsevier Ltd. All rights reserved.

引用

页码：1181 / 1187

页数：7

共 16 条

[1]

Berinde V., 1997, CONTRACTII GEN APLIC, V22

[2]

Kirk W.A., 2003, Fixed Point Theory, V4, P79

[3]

Kirk WA, 2001, HANDBOOK OF METRIC FIXED POINT THEORY, P1

[4]

PILJUGIN SJ, 1999, SHADOWING DYNAMICAL

[5]

Reich S., 2011, Far East J. Math. Sci. Special Volume, P393, DOI DOI 10.1007/S10013-017-0251-1

[6] COMPARISON OF VARIOUS DEFINITIONS OF CONTRACTIVE MAPPINGS [J].

RHOADES, BE .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1977, 226 (FEB) :257-290

[7]

Rhoades BE, 2007, CARPATHIAN J MATH, V23, P11

[8]

Rus I.A., 2008, Topics in Mathematics, Computer Science and Philosophy, P173

[9]

Rus I.A., 2003, Sci. Math. Jpn., V58, P191

[10]

Rus I.A., 2008, Fixed Point Theory

← 1 2 →