Stable Iteration Procedures in Metric Spaces which Generalize a Picard-Type Iteration

نویسنده

  • M. De la Sen
چکیده

This paper investigates the stability of iteration procedures defined by continuous functions acting on self-maps in continuous metric spaces. Some of the obtained results extend the contraction principle to the use of altering-distance functions and extended altering-distance functions, the last ones being piecewise continuous. The conditions for themaps to be contractive for the achievement of stability of the iteration process can be relaxed to the fulfilment of being large contractions or to be subject to altering-distance functions or extended altering functions.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

T-Stability of Picard Iteration in Metric Spaces

Let X, d be a complete metric space and T a self-map of X. Let xn 1 f T, xn be some iteration procedure. Suppose that F T , the fixed point set of T , is nonempty and that xn converges to a point q ∈ F T . Let {yn} ⊂ X and define n d yn 1, f T, yn . If lim n 0 implies that limyn q, then the iteration procedure xn 1 f T, xn is said to be T -stable. Without loss of generality, we may assume that ...

متن کامل

On some fixed points properties and convergence theorems for a Banach operator in hyperbolic spaces

In this paper, we prove some fixed points properties and demiclosedness principle for a Banach operator in uniformly convex hyperbolic spaces. We further propose an iterative scheme for approximating a fixed point of a Banach operator and establish some strong and $Delta$-convergence theorems for such operator in the frame work of uniformly convex hyperbolic spaces. The results obtained in this...

متن کامل

A characterization of the convergence of Picard iteration to a fixed point for a continuous mapping and an application

Necessary and sufficient conditions for the convergence of Picard iteration to a fixed point for a continuous mapping in metric spaces are established. As application, we prove the convergence theorem of Ishikawa iteration to a fixed point for a nonexpansive mapping in Banach spaces. 2004 Elsevier Inc. All rights reserved.

متن کامل

On Rates of Convergence in Metric Fixed Point Theory

This thesis investigates some effective and quantitative aspects of metric fixed point theory in the light of methods from proof theory. The thesis consists of contributions to the program of proof mining, as developed by Kohlenbach and various collaborators since the early 1990s (but with roots back to Kreisel’s program “unwinding of proofs” from the 1950s). The contributions involve both case...

متن کامل

On the Convergence of Ishikawa Type Iteration with Errors to a Common Fixed Point of Two Mappings in Convex Metric Spaces

Abstract In this paper, we study the Ishikawa type iteration process with errors, which converges to a common fixed point of a pair of mappings in complete generalized convex metric spaces. Furthermore, we obtain the corresponding results in Banach spaces. Our result improve and generalize a recent result of Khan[S.H. Khan, Common fixed points of two quasi-contractive operators in normed spaces...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2010