Simpler is also better in approximating fixed points

2021

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Journal of Mathematics and Statistics, 2006

In this study, we establish some stability results for the Krasnoselskij and the Ishikawa iteration procedures. We employ the same method as in Berinde , but using a more general contractive definition than those of Berinde , Rhoades , Harder and Hicks and Osilike .

Applied Mathematics and Computation, 2006

The problem of convergence of the fixed point iterative method has been studied in this article. The main object of this article is to improve the convergence so that the number of iterations is reduced to just few iterations. A technique is presented to increase the order of convergence as much as desired. To illustrate the ability of this technique, some examples, for which regular method needs many times of iterations, are presented.

2016

In this paper, we have done the literature review on stability results of fixed point iteration procedure using different contraction conditions in various spaces.

In metric spaces, several iterative processes have been defined by researchers to approximate the fixed points of different operators. In this paper, we present a qualitative study of Agarwal et al. iteration procedure for fixed points approximation. Some numerical results are presented too. An analytical expression for the number of iterations depending on α and β were obtained.

Advances in Mathematics Scientific Journal, 2021

In this paper, we introduce a new three steps iteration process, prove that our newly proposed iterative scheme can be used to approximate the fixed point of a contractive-like mapping and establish some convergence results for our newly proposed iterative scheme generated by a mapping satisfying condition (E) in the framework of uniformly convex Banach space. In addition, with the aid of numerical examples, we established that our newly proposed iterative scheme is faster than the iterative process introduced by Ullah et al., [26], Karakaya et al., [16], Abass et. al. [1] and some existing iterative scheme in literature. More so, the stability of our newly proposed iterative process is presented and we also gave some numerical examples to display the efficiency of our proposed algorithm

La Matematica

In this paper, a new contraction mapping is introduced which is a generalization of many different contractions. The definition involves a simulation function as well as rational terms. The main results are fixed point results obtained under certain metric and order theoretic conditions. An illustrative example is discussed. Several well known fixed point theorems are shown to be unified by the main theorems. There is a discussion on error estimation and propagation associated with the fixed point iteration. The methodology is a combination of analytic and order theoretic approaches.

Springer eBooks, 2007

The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.

We propose a new iterative algorithm and prove strong and weak convergence theorems for computing fixed points of nonexpansive mappings in a Banach space. We showed that our iteration process is faster than Picard, Mann and S iteration processes. Our results are applied for finding solutions of variational inequality problem.

2020