Jul 21, 2015 recently, the concept of b metric like spaces which is a generalization of metric like spaces and b metric spaces and partial metric spaces was introduced in. Fixed point theory in probabilistic metric spaces request pdf. Topics in fixed point theory saleh almezel springer. Our fixed point theorems, even in the case of partial metric spaces, generalize and improve some. Hadzic, fixed point theory in probabilistic metric spaces, serbian academy of sciences and arts, branch and novi sad, university of novi sad, institute of mathematics, novi sad, 1995.
Subsequently, as an application of our results, in sections 5, we provide an example and prove a fixed point theorem in b metric spaces. Download a study on fixed point theory and its applications. Suranjoy singhs a study on fixed point theory and its applications for your kindle, tablet, ipad, pc or mobile. The concept of a cone b metric space has been introduced recently as a generalization of a b metric space and a cone metric space in 2011. An introduction to metric spaces and fixed point theory. Metric spaces are playing an increasing role in mathematics and the applied sciences. On fixed point theory in partial metric spaces springerlink. In this article, we utilize the notions of the property e. An introduction to metric spaces 1st edition dhananjay.
Istratescu, fixed point theory, an introduction, d. Fixed point theory and applications this is a new project which consists of having a complete book on fixed point theory and its applications on the web. Introduction and preliminaries fixed point theory plays one of the important roles in nonlinear analysis. Distance and coupled fixed point in g metric spaces. An introduction to metric spaces and fixed point theory wiley. The text is selfcontained for a reader with a modest knowledge of the metric fixed point theory. A nemytskiiedelstein type fixed point theorem for partial metric. Over the past two decades the development of fixed point theory in metric spaces has attracted considerable attention due to numerous applications in areas such as variational and linear inequalities, optimization, and approximation theory. Fixed point theorems fixed point theorems concern maps f of a set x into itself that, under certain conditions, admit a. Pdf the class of jscontractions in branciari metric spaces.
An introduction to metric spaces and fixed point theory request. As we have mentioned before, we are interested in extending metric fixed point theorems for the socalled weakly contractive mappings and weakly kannan mappings to the context of partial metric spaces. As an application, we derive some new fixed point results in partial metric spaces. Some coupled fixed point theorems in quasipartial metric. In these metric spaces notes pdf, you will study the concepts of analysis which evidently rely on the notion of distance. Mathematics and is associated to applied mathematics and humanities department, s v national institute of technology, surat, gujarat, india. Fixed point theorems on multi valued mappings in bmetric. A primary aim of this monograph is to stimulate interest among scientists and students in this fascinating field. Rectangular cone bmetric spaces over a banach algebra are introduced as a generalization of metric space and many of its generalizations. This monograph provides a concise introduction to the main results and methods of the fixed point theory in modular function spaces. We then show that soft metric extensions of several important fixed point theorems for metric spaces can be directly deduced from comparable existing results.
A comprehensive, basic level introduction to metric spaces and fixed point theory an introduction to metric spaces and fixed point theory presents a highly selfcontained treatment of the subject that is accessible for students and researchers from diverse mathematical backgrounds, including those who may have had little training in mathematics beyond calculus. An introduction to metric spaces and fixed point theory includes an extensive bibliography and an appendix which provides a complete summary of the concepts of set theory, including zorns lemma, tychonoffs theorem, zermelos theorem, and transfinite induction. Aminiharandi fixed point theory and applications 2012, 2012. An introduction to metric spaces and fixed point theory by. Though there are thousands of fixed point theorems in metric spaces, our theorem is a new type of theorem. It is intended to be especially useful to those who might not have ready access to other sources, or to groups of people with diverse mathematical backgrounds. Introduction an introduction to metric spaces and fixed. In this course, the objective is to develop the usual idea of distance into an abstract form on any set of objects. Banachs contraction principle let m,d be a complete metric space and let t. Any linearly ordered space that is connected and has a top and a bottom element is a fixed point space. Fixed point theory in distance spaces william kirk springer.
An introduction to metric spaces and fixed point theory free epub, mobi, pdf ebooks download, ebook torrents download. The proposed theorems expand and generalize several wellknown comparable results in the literature to ordered cone b metric spaces. An introduction to metric spaces and fixed point theory presents a highly selfcontained treatment of the subject that is accessible for students and researchers from diverse mathematical backgrounds, including those who may have had little training in mathematics beyond calculus. Some fixed point theorems in b metriclike spaces fixed. Common fixed point theorems in modified intuitionistic. The banachs fixed point theory, widely known as the contraction principle, is an important tool in the theory of metric spaces 14, 22. Download for offline reading, highlight, bookmark or take notes while you read an introduction to metric spaces and fixed point theory. He is devoted to general research on the theory of fuzzy sets and fuzzy logic, modules and metric fixed point. Fixed point theory in modular function spaces mohamed a. A generalization of fixed point theorems in smetric spaces. Fixed point theory in complete metric spaces with applications. Moreover the concepts of metric subspace, metric superspace, isometry i.
It provides uptodate coverage of the properties of metric spaces and banach spaces, as well as a detailed. Fixed point and common fixed point theorems on ordered cone b. In mathematics, the banachcaccioppoli fixedpoint theorem also known as the contraction mapping theorem or contractive mapping theorem is an important tool in the theory of metric spaces. On the fixed point theory of soft metric spaces springerlink. Note that, in the definition, we could easily have disposed of the condition that the space is hausdorff. We prove a generalization of edelsteins fixed point theorem.
Key topics covered include banach contraction theorem, hyperconvex metric spaces, modular function spaces, fixed point theory in ordered sets, topological fixed point theory for setvalued maps, coincidence theorems, lefschetz and nielsen theories, systems of nonlinear inequalities, iterative methods for fixed point problems, and the ekeland. Very recently, jleli and samet fixed point theory appl. In this paper, we continue the study of contractive conditions for mappings in complete partial metric spaces. On fixedpoint theorems in fuzzy metric spaces sciencedirect. In particular, and in the light of the both previous results, our objective in this paper is threefold. A generalization of fixed point theorems in s metric spaces. Shubham yadav is currently a student of integrated m. In this paper, we prove a fixed point theorem and a common fixed point theorem for multi valued mappings in complete b metric spaces. This text is primarily an introduction to metric spaces and fixed point theory. Presents a concise accessible document which can be used as an introduction to the subject and its central themes, featuring material collected in a single volume for the first time. Fixed point theory in probabilistic metric spaces can be considered as a part of probabilistic analysis, which is a very dynamic area of mathematical research. The first fixed point theorem in probabilistic metric spaces was proved by sehgal and baruchareid 272 for mappings f.
Inspired by the interest aroused by fixed point theory in partial metric spaces, in the present paper, we focus our study on the possibility of extending some metric fixed point theorems for the socalled weakly contractive mappings and weakly kannan mappings to the context of partial metric spaces. In section 4, we prove the main theorem in this paper, i. Available at a lower price from other sellers that may not offer free prime shipping. Written by a team of leading experts in the field, this volume presents a selfcontained account of the theory, techniques and results in metric type spaces in particular in g metric spaces. An introduction to metric spaces and fixed point theory mohamed. Fixed point theorems with applications to economics and game theory. We introduce the notions of a weakly contractive mapping and a weakly kannan mapping in. Under the assumptions of corollary 5, we have, by virtue remark 3, that sequence tx, converges to the unique fixed point of i. This process is experimental and the keywords may be updated as the learning algorithm improves. Shahzad and valero fixed point theory and applications 2015 2015. Introduction to metric fixed point theory in these lectures, we will focus mainly on the second area though from time to time we may say a word on the other areas. Metriclike spaces, partial metric spaces and fixed points core. Jan 28, 2016 the aim of this paper is to show that a soft metric induces a compatible metric on the collection of all soft points of the absolute soft set, when the set of parameters is a finite set.
Probabilistic b metric spaces and nonlinear contractions. Covers four classical fixed point theorems against which metric extensions are usually checked and several new modern theorems on fixed point theory and distances. Concretely, we present fixed point results for weakly contractive and weakly kannan mappings in such a way that the classical metric counterpart results are retrieved as a particular case. Detailed coverage of the newest developments in metric spaces and fixed point.
The aim of this paper is to establish some fixed point and common fixed point theorems on ordered cone b metric spaces. A new type of fixed point theorem in metric spaces. In nonlinear functional analysis, fixed point theory is indispensable due to its wide application. Modular function spaces are natural generalizations of both function and sequence variants of many important spaces like lebesgue, orlicz, musielakorlicz, lorentz. The aim of this paper is to introduce new concepts of complete metric space and continuous function and establish fixed point results for modified rational contraction mappings in complete metric spaces. Khamsi and others published an introduction to metric spaces and fixed point theory find, read and cite all the research. Buy an introduction to metric spaces and fixed point theory on. An introduction to metric spaces and fixed point theory includes an extensive bibliography and an appendix which provides a complete summary of the concepts of set theory, including zorns lemma, tychonoffs theorem, zermelos theorem, and transfi. An introduction to metric spaces and fixed point theory ebook written by mohamed a. Get your kindle here, or download a free kindle reading app. On fixed point theory in partial metric spaces fixed point.
In this paper, we establish some existence results of. Features an extensive bibliography for outside reading. Mar 25, 2015 banach space nonexpansive mapping common fixed point fixed point theory convex banach space these keywords were added by machine and not by the authors. The introduction of the common limit range property on v fuzzy metric spaces is the foremost aim of this paper.
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