A NOTE ON DEVELOPMENT OF METRIC FIXED POINT THEORY

Many problems in pure and applied mathematics have as their solutions the fixed point of some mapping F . Therefore a number of procedures in numerical analysis and approximations theory amount to obtaining successive approximations to the fixed point of an approximate mapping. Our object in this paper to discuss about fixed point theory and its applications in metric spaces, also we established some fixed point theorems in complete metric spaces, which generalized many results of great mathematicians.

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

In this paper we prove a fixed point theorem for -generalized contractions and obtain its consequences. KEYWORDS: D*-metric space,K-contraction,  − í µí±”í µí±’í µí±›í µí±’í µí±Ÿí µí±Ží µí±™í µí±–í µí± §í µí±’í µí±‘ í µí±í µí±œí µí±›í µí±¡í µí±Ÿí µí±Ží µí±í µí±¡í µí±–í µí±œí µí±› .

Analele Universitatii "Ovidius" Constanta - Seria Matematica

In this paper, we introduce the notion of α-ψ-contractive mapping of type E, to remedy of the weakness of the existing contraction mappings. We investigate the existence and uniqueness of a fixed point of such mappings. We also list some examples to illustrate our results that unify and generalize the several well-known results including the famous Banach contraction mapping principle.

Mathematical theory and modeling, 2013

In this paper we prove some fixed point theorem in metric space by using altering distance function. AMS Subject Classification: 47H10, 54H25 . Keywords: Metric space, fixed point, common fixed point, altering distance function.

Hacettepe Journal of Mathematics and Statistics, 2017

Recently, Wardowski in [Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl. 2012] introduced the concept of F-contraction on complete metric space which is a proper generalization of Banach contraction principle. In the present paper, we proved a related fixed point theorem with F-contraction mappings on two complete metric spaces.

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.

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.

2018

In a recent paper [Pata, V., A fixed point theorem in metric spaces, J. Fixed Point Theory Appl., 10 (2011), No. 2, 299–305], the author stated and proved a fixed point theorem that is intended to generalize the well known Banach’s contraction mapping principle. In this note we show that the main result in the above paper does not hold at least in two extremal cases for the parameter ε involved in the contraction condition used there. We also present some illustrative examples and related results.

Mathematical Sciences Letters, 2014

In this paper, our purpose is to give a new generalization of Kannan's type and Chatterjea's type fixed point theorems in metric spaces. We have two main ideas. Our first idea is applying the logic of Choudhury [5] to the Kannan type contraction mappings, the second is applying the logic of Dutta and Choudhury [6] to the Kannan type contraction mappings and Chatterjea type contraction mappings.