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Fixed Point Results In Dislocated And Dislocated Quasi Metric Spaces
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Book Synopsis Fixed Point Results in Dislocated and Dislocated Quasi Metric Spaces by : Dinesh Panthi
Download or read book Fixed Point Results in Dislocated and Dislocated Quasi Metric Spaces written by Dinesh Panthi and published by LAP Lambert Academic Publishing. This book was released on 2013 with total page 68 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fixed point theory is a part of non-linear analysis since 1960 in the field of mathematics as it provides the necessary tools to have existence theorems in many different non-linear problems. Although Dutch mathematician L.E.J Brouwer established the first fixed point theorem but the credit of making concept useful and popular goes to Polish mathematician S. Banach in 1922 who proved famous Banach contraction mapping principle. The notion of dislocated metric space was first time introduced in 1986 under the name of metric domains. Dislocated quasi metric space was introduced in 2006 as a generalization of important theorems of dislocated metric space. These spaces are important extensions of metric space and play important roles for the development of non-linear analysis. This research work investigates some fixed point theorems in these spaces which extend and unify some well-known similar results in the literature. A survey work on some fixed point theorems of asymptotic contractions in metric space has also been presented. This work should be especially useful to young researchers and anyone else who work in the field of non linear analysis.
Book Synopsis Higher-Order Fixed Point Theory in Dislocated Metric Spaces Under r-Compatibility of Mappings and Related Concepts by : Clement Ampadu
Download or read book Higher-Order Fixed Point Theory in Dislocated Metric Spaces Under r-Compatibility of Mappings and Related Concepts written by Clement Ampadu and published by Lulu.com. This book was released on 2018-02-19 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt: We consider the relationship between when the r-times composition of two maps commute, and the concepts of coincidence point, weakly compatible mappings, (EA)-property, (EA)-like property, and compatible mappings of type (A), and obtain some higher-order fixed point theorems in the sense of [Clement Ampadu, Fixed Point Theory for Higher-Order Mappings. ISBN: 5800118959925, lulu.com, 2016]
Book Synopsis On Neutrosophic Triplet quasi-dislocated-b-metric space by : Anuradha
Download or read book On Neutrosophic Triplet quasi-dislocated-b-metric space written by Anuradha and published by Infinite Study. This book was released on 2020-12-01 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt: The concept of neutrosophic triplet firstly introduced by F. Smarandache and M. Ali. This notion (neutrosophic triplet) is a group of three elements that satisfy certain properties with some binary operation. These neutrosophic triplets highly depends on the proposed binary operation. In this article, we make some observations concerning Neutrosophic triplet metric space (NTMS), Neutrosophic triplet partial metric space (NTPMS), Neutrosophic triplet-b-metric space (NT-b-MS) introduced by Sahin et al. and put our observation on the definitions defined in these articles. Moreover, inspired by Ur Rahaman and Sahin et al. further we define a new topological construction named as Neutrosophic Triplet quasi-dislocated b-metric space (NT-qdb-MS) and study some properties of NT-qdb-MS. Furthermore using this construction, we establish some fixed point theorems in the context of NT-qdb-MS using graph. For the validity of our results, we also provide an example.
Book Synopsis Fixed Point Results in W-Distance Spaces by : Vladimir Rakočević
Download or read book Fixed Point Results in W-Distance Spaces written by Vladimir Rakočević and published by CRC Press. This book was released on 2021-12-30 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fixed Point Results in W-Distance Spaces is a self-contained and comprehensive reference for advanced fixed-point theory and can serve as a useful guide for related research. The book can be used as a teaching resource for advanced courses on fixed-point theory, which is a modern and important field in mathematics. It would be especially valuable for graduate and postgraduate courses and seminars. Features Written in a concise and fluent style, covers a broad range of topics and includes related topics from research. Suitable for researchers and postgraduates. Contains brand new results not published elsewhere.
Book Synopsis Fixed Point Theory in Metric Spaces by : Praveen Agarwal
Download or read book Fixed Point Theory in Metric Spaces written by Praveen Agarwal and published by Springer. This book was released on 2018-10-13 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a detailed study of recent results in metric fixed point theory and presents several applications in nonlinear analysis, including matrix equations, integral equations and polynomial approximations. Each chapter is accompanied by basic definitions, mathematical preliminaries and proof of the main results. Divided into ten chapters, it discusses topics such as the Banach contraction principle and its converse; Ran-Reurings fixed point theorem with applications; the existence of fixed points for the class of α-ψ contractive mappings with applications to quadratic integral equations; recent results on fixed point theory for cyclic mappings with applications to the study of functional equations; the generalization of the Banach fixed point theorem on Branciari metric spaces; the existence of fixed points for a certain class of mappings satisfying an implicit contraction; fixed point results for a class of mappings satisfying a certain contraction involving extended simulation functions; the solvability of a coupled fixed point problem under a finite number of equality constraints; the concept of generalized metric spaces, for which the authors extend some well-known fixed point results; and a new fixed point theorem that helps in establishing a Kelisky–Rivlin type result for q-Bernstein polynomials and modified q-Bernstein polynomials. The book is a valuable resource for a wide audience, including graduate students and researchers.
Book Synopsis Fixed Point Theory in Metric Type Spaces by : Ravi P. Agarwal
Download or read book Fixed Point Theory in Metric Type Spaces written by Ravi P. Agarwal and published by Springer. This book was released on 2016-03-24 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by a team of leading experts in the field, this volume presents a self-contained account of the theory, techniques and results in metric type spaces (in particular in G-metric spaces); that is, the text approaches this important area of fixed point analysis beginning from the basic ideas of metric space topology. The text is structured so that it leads the reader from preliminaries and historical notes on metric spaces (in particular G-metric spaces) and on mappings, to Banach type contraction theorems in metric type spaces, fixed point theory in partially ordered G-metric spaces, fixed point theory for expansive mappings in metric type spaces, generalizations, present results and techniques in a very general abstract setting and framework. Fixed point theory is one of the major research areas in nonlinear analysis. This is partly due to the fact that in many real world problems fixed point theory is the basic mathematical tool used to establish the existence of solutions to problems which arise naturally in applications. As a result, fixed point theory is an important area of study in pure and applied mathematics and it is a flourishing area of research.
Book Synopsis Recent Advances on Quasi-Metric Spaces by : Andreea Fulga
Download or read book Recent Advances on Quasi-Metric Spaces written by Andreea Fulga and published by . This book was released on 2020 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: Metric fixed-point theory lies in the intersection of three main subjects: topology, functional analysis, and applied mathematics. The first fixed-point theorem, also known as contraction mapping principle, was abstracted by Banach from the papers of Liouville and Picard, in which certain differential equations were solved by using the method of successive approximation. In other words, fixed-point theory developed from applied mathematics and has developed in functional analysis and topology. Fixed-point theory is a dynamic research subject that has never lost the attention of researchers, as it is very open to development both in theoretical and practical fields. In this Special Issue, among several submissions, we selected eight papers that we believe will be interesting to researchers who study metric fixed-point theory and related applications. It is great to see that this Special Issue fulfilled its aims. There are not only theoretical results but also some applications that were based on obtained fixed-point results. In addition, the presented results have great potential to be improved, extended, and generalized in distinct ways. The published results also have a wide application potential in various qualitative sciences, including physics, economics, computer science, engineering, and so on.
Book Synopsis The Extension of Some Results on Fixed Points in Abstract Spaces by : Neeraj Malviya
Download or read book The Extension of Some Results on Fixed Points in Abstract Spaces written by Neeraj Malviya and published by LAP Lambert Academic Publishing. This book was released on 2012 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the first chapter we introduced fixed point, fixed point theory and its applications.In chapters two and three we prove some random fixed point theorems for contractive and expansive type mappings in Hilbert space.In the chapter four we present some common fixed point theorems for rational and other inequalities involving expansive type mappings in Hilbert space.In chapter five we generalize and unify the results of Hardy and Rogers using asymptotically regular maps and sequence.In chapter six results of fixed point in an e-chainable metric space have been established and for this we have used general contractive conditions.In chapter seven we prove the chainability of points and sets is a product invariant property and finally a fixed point theorem is proved.In chapter eight we define asymptotically regular maps and sequence in cone metric spaces and the existence of fixed points for asymptotically regular maps on cone metric spaces is investigated.In chapter nine the existence of fixed point for continuous maps on dislocated metric spaces is investigated.In the last chapter we define Pseudo-2-metric spaces and Pseudo-2-metric product spaces.
Book Synopsis Recent Advances on Quasi-Metric Spaces by : Andreea Fulga
Download or read book Recent Advances on Quasi-Metric Spaces written by Andreea Fulga and published by MDPI. This book was released on 2020-06-03 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: Metric fixed-point theory lies in the intersection of three main subjects: topology, functional analysis, and applied mathematics. The first fixed-point theorem, also known as contraction mapping principle, was abstracted by Banach from the papers of Liouville and Picard, in which certain differential equations were solved by using the method of successive approximation. In other words, fixed-point theory developed from applied mathematics and has developed in functional analysis and topology. Fixed-point theory is a dynamic research subject that has never lost the attention of researchers, as it is very open to development both in theoretical and practical fields. In this Special Issue, among several submissions, we selected eight papers that we believe will be interesting to researchers who study metric fixed-point theory and related applications. It is great to see that this Special Issue fulfilled its aims. There are not only theoretical results but also some applications that were based on obtained fixed-point results. In addition, the presented results have great potential to be improved, extended, and generalized in distinct ways. The published results also have a wide application potential in various qualitative sciences, including physics, economics, computer science, engineering, and so on.
Book Synopsis Fixed Point Theory for Weakly Contractive Maps Defined Implicitly Using Multiplicative C-class Functions by : Clement Ampadu
Download or read book Fixed Point Theory for Weakly Contractive Maps Defined Implicitly Using Multiplicative C-class Functions written by Clement Ampadu and published by Lulu.com. This book was released on 2017-05-08 with total page 41 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this monograph we have defined the multiplicative version of weakly contractive mappings implicitly via the multiplicative C-class function and obtained some fixed point theorems for such mappings in the multiplicative analogue of various spaces. A nice feature of this monograph are the (publishable) exercise set, which begs the reader to explore the beautiful connection between weakly contractive mappings, c-class function, and their multiplicative analogue.
Book Synopsis Advances in Nonlinear Analysis via the Concept of Measure of Noncompactness by : Józef Banaś
Download or read book Advances in Nonlinear Analysis via the Concept of Measure of Noncompactness written by Józef Banaś and published by Springer. This book was released on 2017-04-25 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a comprehensive treatment of the theory of measures of noncompactness. It discusses various applications of the theory of measures of noncompactness, in particular, by addressing the results and methods of fixed-point theory. The concept of a measure of noncompactness is very useful for the mathematical community working in nonlinear analysis. Both these theories are especially useful in investigations connected with differential equations, integral equations, functional integral equations and optimization theory. Thus, one of the book’s central goals is to collect and present sufficient conditions for the solvability of such equations. The results are established in miscellaneous function spaces, and particular attention is paid to fractional calculus.
Book Synopsis Handbook of Metric Fixed Point Theory by : W.A. Kirk
Download or read book Handbook of Metric Fixed Point Theory written by W.A. Kirk and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 702 pages. Available in PDF, EPUB and Kindle. Book excerpt: Metric fixed point theory encompasses the branch of fixed point theory which metric conditions on the underlying space and/or on the mappings play a fundamental role. In some sense the theory is a far-reaching outgrowth of Banach's contraction mapping principle. A natural extension of the study of contractions is the limiting case when the Lipschitz constant is allowed to equal one. Such mappings are called nonexpansive. Nonexpansive mappings arise in a variety of natural ways, for example in the study of holomorphic mappings and hyperconvex metric spaces. Because most of the spaces studied in analysis share many algebraic and topological properties as well as metric properties, there is no clear line separating metric fixed point theory from the topological or set-theoretic branch of the theory. Also, because of its metric underpinnings, metric fixed point theory has provided the motivation for the study of many geometric properties of Banach spaces. The contents of this Handbook reflect all of these facts. The purpose of the Handbook is to provide a primary resource for anyone interested in fixed point theory with a metric flavor. The goal is to provide information for those wishing to find results that might apply to their own work and for those wishing to obtain a deeper understanding of the theory. The book should be of interest to a wide range of researchers in mathematical analysis as well as to those whose primary interest is the study of fixed point theory and the underlying spaces. The level of exposition is directed to a wide audience, including students and established researchers.
Book Synopsis Fixed Point Theory in Distance Spaces by : William Kirk
Download or read book Fixed Point Theory in Distance Spaces written by William Kirk and published by Springer. This book was released on 2014-10-23 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a monograph on fixed point theory, covering the purely metric aspects of the theory–particularly results that do not depend on any algebraic structure of the underlying space. Traditionally, a large body of metric fixed point theory has been couched in a functional analytic framework. This aspect of the theory has been written about extensively. There are four classical fixed point theorems against which metric extensions are usually checked. These are, respectively, the Banach contraction mapping principal, Nadler’s well known set-valued extension of that theorem, the extension of Banach’s theorem to nonexpansive mappings, and Caristi’s theorem. These comparisons form a significant component of this book. This book is divided into three parts. Part I contains some aspects of the purely metric theory, especially Caristi’s theorem and a few of its many extensions. There is also a discussion of nonexpansive mappings, viewed in the context of logical foundations. Part I also contains certain results in hyperconvex metric spaces and ultrametric spaces. Part II treats fixed point theory in classes of spaces which, in addition to having a metric structure, also have geometric structure. These specifically include the geodesic spaces, length spaces and CAT(0) spaces. Part III focuses on distance spaces that are not necessarily metric. These include certain distance spaces which lie strictly between the class of semimetric spaces and the class of metric spaces, in that they satisfy relaxed versions of the triangle inequality, as well as other spaces whose distance properties do not fully satisfy the metric axioms.
Book Synopsis Fixed Point Theory and Variational Principles in Metric Spaces by : Qamrul Hasan Ansari
Download or read book Fixed Point Theory and Variational Principles in Metric Spaces written by Qamrul Hasan Ansari and published by Cambridge University Press. This book was released on 2023-08-31 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: A book covering theory and examples for undergraduates, graduates, and researchers studying fixed point theory or nonlinear analysis.
Book Synopsis Fixed Point Theory and Related Topics by : Hsien-ChungWu
Download or read book Fixed Point Theory and Related Topics written by Hsien-ChungWu and published by MDPI. This book was released on 2020-03-13 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fixed point theory arose from the Banach contraction principle and has been studied for a long time. Its application mostly relies on the existence of solutions to mathematical problems that are formulated from economics and engineering. After the existence of the solutions is guaranteed, the numerical methodology will be established to obtain the approximated solution. Fixed points of function depend heavily on the considered spaces that are defined using the intuitive axioms. In particular, variant metrics spaces are proposed, like a partial metric space, b-metric space, fuzzy metric space and probabilistic metric space, etc. Different spaces will result in different types of fixed point theorems. In other words, there are a lot of different types of fixed point theorems in the literature. Therefore, this Special Issue welcomes survey articles. Articles that unify the different types of fixed point theorems are also very welcome. The topics of this Special Issue include the following: Fixed point theorems in metric space Fixed point theorems in fuzzy metric space Fixed point theorems in probabilistic metric space Fixed point theorems of set-valued functions in various spaces The existence of solutions in game theory The existence of solutions for equilibrium problems The existence of solutions of differential equations The existence of solutions of integral equations Numerical methods for obtaining the approximated fixed points
Book Synopsis Higher-Order Fixed Point Theory in Partial Metric Spaces: Some Results Generalizing the Hardy-Rogers Map by : Clement Ampadu
Download or read book Higher-Order Fixed Point Theory in Partial Metric Spaces: Some Results Generalizing the Hardy-Rogers Map written by Clement Ampadu and published by Lulu.com. This book was released on 2016-11-26 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first to present a systematic study of higher-order fixed point theory on partial metric spaces. People working in fixed point theory with interest in partial metric spaces will find it useful in their research and teaching activities with graduate students, post-doctoral faculty, and professors
Book Synopsis Theory and Application of Fixed Point by : Erdal Karapinar
Download or read book Theory and Application of Fixed Point written by Erdal Karapinar and published by Mdpi AG. This book was released on 2021-09-30 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the past few decades, several interesting problems have been solved using fixed point theory. In addition to classical ordinary differential equations and integral equation, researchers also focus on fractional differential equations (FDE) and fractional integral equations (FIE). Indeed, FDE and FIE lead to a better understanding of several physical phenomena, which is why such differential equations have been highly appreciated and explored. We also note the importance of distinct abstract spaces, such as quasi-metric, b-metric, symmetric, partial metric, and dislocated metric. Sometimes, one of these spaces is more suitable for a particular application. Fixed point theory techniques in partial metric spaces have been used to solve classical problems of the semantic and domain theory of computer science. This book contains some very recent theoretical results related to some new types of contraction mappings defined in various types of spaces. There are also studies related to applications of the theoretical findings to mathematical models of specific problems, and their approximate computations. In this sense, this book will contribute to the area and provide directions for further developments in fixed point theory and its applications.
