A sufficient and necessary condition for the convergence of the sequence of successive approximations to a unique fixed point-Reference-Cited by-同舟云学术

A sufficient and necessary condition for the convergence of the sequence of successive approximations to a unique fixed point

Published:2008-06-04 Issue:11 Volume:136 Page:4089-4093
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Suzuki Tomonari

Abstract

If ( X , d ) (X, d) is a complete metric space and T : X → X T : X \to X is a contraction mapping, then the conclusion of the Banach-Caccioppoli contraction principle is that the sequence of successive approximations of T T starting from any point of the space converges to a unique fixed point. In this paper, we obtain a sufficient and necessary condition of the above conclusion in terms of the so-called strong Leader mappings.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/2008-136-11/S0002-9939-08-09390-8/S0002-9939-08-09390-8.pdf

Reference18 articles.

1. S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math., 3 (1922), 133–181.

2. R. Caccioppoli, Un teorema generale sull’esistenza di elementi uniti in una transformazione funzionale, Rend. Accad. Naz. Lincei, 11 (1930), 794–799.

3. Fixed point theorems for mappings satisfying inwardness conditions;Caristi, James;Trans. Amer. Math. Soc.,1976

4. Geometric fixed point theory and inwardness conditions;Caristi, James,1975

5. A generalization of Banach’s contraction principle;Ćirić, Lj. B.;Proc. Amer. Math. Soc.,1974

Cited by 5 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. A sufficient and necessary condition for the convergence of the sequence of successive approximations to a unique fixed point II;FIXED POINT THEORY A;2015

2. Two New Types of Fixed Point Theorems in Complete Metric Spaces;Abstract and Applied Analysis;2014

3. Convergence of the Sequence of Successive Approximations to a Fixed Point;Fixed Point Theory and Applications;2010

4. A new type of fixed point theorem in metric spaces;Nonlinear Analysis: Theory, Methods & Applications;2009-12

5. Subrahmanyam’s fixed point theorem;Nonlinear Analysis: Theory, Methods & Applications;2009-09