Some common fixed point theorems in normed linear spaces

Ibn AL-Haitham Journal For Pure and Applied Sciences

The focus of this article, reviewed a generalized of contraction mapping and nonexpansive maps and recall some theorems about the existence and uniqueness of common fixed point and coincidence fixed-point for such maps under some conditions. Moreover, some schemes of different types as one-step schemes ,two-step schemes and three step schemes (Mann scheme algorithm, Ishukawa scheme algorithm, noor scheme algorithm, .scheme algorithm, scheme algorithm Modified scheme algorithm arahan scheme algorithm and others. The convergence of these schemes has been studied .On the other hands, We also reviewed the convergence, valence and stability theories of different types of near-plots in convex metric space.

TJPRC, 2013

In the present paper, we obtain a unique common fixed point theorem for three self -maps on complete metric space satisfying a new contraction condition which significantly covers the result of Banach [2] (see also [5], [11]). Mathematics Subject Classification: 47H10; 54H25

2009

We prove a theorem to approximate common fixed points of two quasi-contractive operators on a normed space through an iteration process with errors and more general than the Ishikawa iteration process.Our result generalizes and improves upon, among others, the corresponding result of Berinde [1] in the following two different directions: (i) more general iteration process with error terms (ii) wider class of mappings.

https://www.ijrrjournal.com/IJRR_Vol.3_Issue.7_July2016/Abstract_IJRR009.html, 2016

A map has a fixed point at P. If fixed point theorems have useful applications in analysis. Some of the iterative methods which have been studied are related to S. Banach, W.R. Mann, J. Riemermann, W.G. Dastonand a host of other mathematics. Studies by Prof. S. Ishikawa and Prof. B.E. Rhoads, throw new light on the iteration process of W.R. Mann, Prof. Ishikawa studied by the following iteration process. For a subset E of an Ailbert space H, if and only if the sequence generated by Where (c n) are real sequence in [0, 1].

2015

Abstract. In this paper, we establish some common fixed point theorems for selfmappings in uniform spaces by employing the concepts of an A-distance, an E-distance as well as the notion of comparison function. A more general contractive condition than that used to establish some of the results of Aamri and El Moutawakil [1] is employed to obtain our results. Our results are generalizations of some of the results of [1]. 1.

Communications in Mathematical Analysis, 2020

Let $ H$ be a Hilbert space and $C$ be a closed, convex and nonempty subset of $H$. Let $T:C rightarrow H$ be a non-self and non-expansive mapping. V. Colao and G. Marino with particular choice of the sequence ${alpha_{n}}$ in Krasonselskii-Mann algorithm, ${x}_{n+1}={alpha}_{n}{x}_{n}+(1-{alpha}_{n})T({x}_{n}),$ proved both weak and strong converging results. In this paper, we generalize their algorithm and result, imposing some conditions upon the set $C$ and finite many mappings from $C$ in to $H$, to obtain a converging sequence to a common fixed point for these non-self and non-expansive mappings.

2017

The purpose of this paper is to prove a common fixed point theorem, by using the concept of weakly subsequential continuity and compatibility of type (E) for two pairs of self mappings satisfying a linear contractive condition in metric spaces, we give two examples to illustrate our results. Full text

Mathematical Sciences, 2013

In this paper, we prove some common fixed point theorems for weakly compatible mappings in metric spaces satisfying generalized (ψ, ϕ)-contractive conditions under the common limit range property. We present a fixed point theorem for four finite families of self-mappings which can be utilized to derive common fixed point theorems involving any number of finite mappings. Our results improve and extend the corresponding results of Radenović et al. (Bull. Iranian Math. Soc. 38(3):625-645, 2012). We also furnish some illustrative examples to support our main results. The concept of weak contraction was introduced by Alber and Guerre-Delabriere [7] in 1997, wherein the authors introduced the following notion for mappings defined on a Hilbert space X. Consider the following set of real functions = { ϕ : [ 0, +∞) →[ 0, +∞) : ϕ is lower semi-continuous and ϕ −1 ({0}) = {0} }.

Analele Universitatii "Ovidius" Constanta - Seria Matematica, 2013

Some fixed point convergence properties are proved for compact and demicompact maps acting over closed, bounded and convex subsets of a real Hilbert space. We also show that for a generalized nonexpansive mapping in a uniformly convex Banach space the Ishikawa iterates converge to a fixed point. Finally, a convergence type result is established for multivalued contractive mappings acting on closed subsets of a complete metric space. These are extensions of results in Ciric, et. al. [7], Panyanak [2] and Agarwal, et. al. [9].

1988

By using a condition of Reich, we establish two fixed point theorems concerning sequences of contractive mappings and their fixed points. A suitable example is also given. KEY WORDS AND PHRASES: Complete metric space, Fixed point, Sequence of mappings. 1980 AMS SUBJECT CLASSIFICATION CODE. 47H10, 54H25. i. INTRODUCTIONS. Throughout this paper, (X,d) denotes a complete metric space and T stands for a mapping of X into itself. It is well known that each of the following conditions ensure the existence and uniqueness of a fixed point of T: (A) (Banach). There exists a number k, 0 & k < I, such that for each x,y in X, d(Tx, Ty)k. d(x,y) (B) (Rakotch [I]). There exists a monotonically decreasing function g: (o,)[0,i) such that for each x,y in X,xy, d(Tx,Ty)g(d(x,y) d(x,y). (C) (Reich [2]). There exist nonnegative numbers a,b such that for each x,y in X,xy, d(Tx,Ty) a.d(x,y) +b. [d(x,Tx)+d(y,Ty].