The contraction principle for mappings on a metric space with a graph

被引：4
|
作者：
Jachymski, Jacek [1 ]
机构：
[1] Tech Univ Lodz, Inst Math, PL-93005 Lodz, Poland
来源：
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2008年 / 136卷 / 04期
关键词：
fixed point; Picard operator; partial order; connected graph; Bernstein operator;
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We give some generalizations of the Banach Contraction Principle to mappings on a metric space endowed with a graph. This extends and subsumes many recent results of other authors which were obtained for mappings on a partially ordered metric space. As an application, we present a theorem on the convergence of successive approximations for some linear operators on a Banach space. In particular, the last result easily yields the Kelisky-Rivlin theorem on iterates of the Bernstein operators on the space C[0, 1].
引用
收藏
页码：1359 / 1373
页数：15
相关论文
共 50 条
  • [1] The contraction principle for mappings on a modular metric space with a graph
    Monther Rashed Alfuraidan
    [J]. Fixed Point Theory and Applications, 2015
  • [2] The contraction principle for mappings on a modular metric space with a graph
    Alfuraidan, Monther Rashed
    [J]. FIXED POINT THEORY AND APPLICATIONS, 2015, : 1 - 10
  • [3] The contraction principle for set valued mappings on a metric space with a graph
    Beg, Ismat
    Butt, Asrna Rashid
    Radojevic, S.
    [J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2010, 60 (05) : 1214 - 1219
  • [4] The Contraction Principle for Multivalued Mappings on a Modular Metric Space with a Graph
    Alfuraidan, Monther Rashed
    [J]. CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 2016, 59 (01): : 3 - 12
  • [5] An Extension of Set-Valued Contraction Principle for Mappings on a Metric Space with a Graph and Application
    Sultana, Asrifa
    Vetrivel, V.
    [J]. NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, 2017, 38 (08) : 1060 - 1068
  • [6] On contraction principles for mappings defined on a metric space with a directed graph
    Boonsri, Narongsuk
    Saejung, Satit
    [J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2024, 530 (01)
  • [7] Banach's Contraction Principle for Nonlinear Contraction Mappings in Modular Metric Spaces
    Martinez-Moreno, Juan
    Sintunavarat, Wutiphol
    Kumam, Poom
    [J]. BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2017, 40 (01) : 335 - 344
  • [8] Banach’s Contraction Principle for Nonlinear Contraction Mappings in Modular Metric Spaces
    Juan Martínez-Moreno
    Wutiphol Sintunavarat
    Poom Kumam
    [J]. Bulletin of the Malaysian Mathematical Sciences Society, 2017, 40 : 335 - 344
  • [9] Banach contraction principle for cyclical mappings on partial metric spaces
    Abdeljawad, T.
    Alzabut, J. O.
    Mukheimer, A.
    Zaidan, Y.
    [J]. FIXED POINT THEORY AND APPLICATIONS, 2012,
  • [10] Banach contraction principle for cyclical mappings on partial metric spaces
    T Abdeljawad
    JO Alzabut
    A Mukheimer
    Y Zaidan
    [J]. Fixed Point Theory and Applications, 2012
12345