On a New Generalization of Banach Contraction Principle with Application (original) (raw)

A Study of Banach Fixed Point Theorem and It’s Applications

American Journal of Computational Mathematics, 2021

This paper aims at treating a study of Banach fixed point theorem for mapping results that introduced in the setting of normed space. The classical Banach fixed point theorem is a generalization of this work. A fixed point theory is a beautiful mixture of Mathematical analysis to explain some conditions in which maps give excellent solutions. Here later many mathematicians used this fixed point theory to establish their results, see for instance, Picard-Lindel of Theorem, The Picard theorem, Implicit function theorem etc. Also, we developed ideas that many of known fixed point theorems can easily be derived from the Banach theorem. It extends some recent works on the extension of Banach contraction principle to metric space with norm spaces.

On Presic Type Extension of Banach Contraction Principle

m-hikari.com

Let (X, d) be a metric space, k a positive integer, T : X k −→ X, f : X −→ X be mappings. In this paper we have investigated under what conditions the mappings f and T will have a common fixed point. Our results extends and generalises the results of [3], [4], [5] and [6].

F eb 2 02 0 Caristi-Banach type contraction via simulation function

2020

In 1922, Polish mathematician Stefan Banach [2] gave a fixed point theorem. It is also known as the Banach Contraction mapping theorem or principle (BCP). It is an important tool in the metric fixed point theory. It confirms the existence and uniqueness of fixed point of certain self maps of metric spaces and provides a constructive method to find fixed points. There are so many extension, generalizations of BCP in different settings and there applications. Among them, In 1976, Caristi [4] proved a fixed point theorem and applied to derive a generalization of the Contraction Mapping Principle in a complete metric space. Recently, In 2019, E. Karapinar et al., [9] give a new fixed point theorem in b metric space which is inspired from both Caristi and Banach. b metric space introduced by Czerwik [5] to generalize the concept of metric space by introducing a real number s ≥ 1 in the triangle inequality of metric space. Inspired by E. Karapinar et al., [9] we introduce the notion of a ...

ON FIXED POINT THEOREM IN WEAK CONTRACTION PRINCIPLE

The study of Fixed Point Theorem has been widely done in many fields. The Banach Fixed Point Theorem plays important role in this theory. It becomes milestone in the various paths in this field. In this paper we have discussed existence and uniqueness of fixed point in more general conditions. The concept of weak contraction mapping over contractive metric space is discussed. In general, for a function f:X ?X to have a fixed point, weak contraction is not a sufficient condition for function. Additionally function needs to be a compact to have a fixed point. Banach contraction principle is one of the directive theorems in the analysis of the result.

Variations of Banach fix point theorem

2006

In the present work we study various consequences and generalizations of Banach fixed point theorem. In the first part, we study consequences of classic contraction principle: sequences of contractive mappigs, several different variations of contractive conditions, several applications in Banach spaces and discrete contraction principle (versions of Eilenberg and Jachymski) and the question of equivalence between discrete principles and Banach theorem. In the second part, there are presented several ways how to generalize Banach theorem: as examples, various fixed point theorems are proven (Edelstein, Bailey, Ćirić, Kirk and others).

Two new types of fixed point theorems for F-contraction

Journal of Advanced Studies in Topology, 2016

The purpose of the present paper is to continue the study of fixed pointtheory in complete metric spaces. Wardowski [Fixed Point Theory Appl. 2012: 94]introduced a new type of contraction called \(F\)-contraction and proved afixed point result in complete metric spaces, which in turn generalize theBanach contraction principle. The aim of this paper is to extend the conceptof FFF-contraction into generalized \(F\)-contraction. An example andapplication are given to illustrate the usability of the main result.

On A Version of The Banach's Fixed Point Theorem1

2008

Banach in 1922 proved the celebrated result which is well-known in the literature as the Banach's Fixed Point Theorem or the Con- traction Mapping Principle. This result of Banach also known as the Theorem of Picard-Banach-Cacciopoli is contained in several mono- graphs including Agarwal et al (1), Berinde (3, 4, 5) and Zeidler (17). In this paper, we shall establish the error estimates as well as the rate of convergence for a version of the Banach's Fixed Point The- orem by employing a certain form of '¡contraction different from that of Berinde (5). Our results are generalizations of those of Banach (2) and Berinde (3, 4, 5)