Characterization Theorems Inspired by the Hardy-Rogers Map II: Some Results in Cone Metric Spaces PDF Download
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Author: Clement Ampadu
Publisher: Lulu.com
ISBN: 1365109917
Category : Science
Languages : en
Pages : 42
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Book Description
The book is suggested as collateral reading for people interested in "fixed point theorems for contractive type mappings". We continue the investigation of the rth-order Hardy Rogers map in the setting of cone metric spaces. Some open problems in the form of exercises are proposed. The reader comes to grasp with the nitty-gritty ideas of pure mathematical modeling in research. Construction of theorems and proof writing is developed. Researchers in fixed point theory and their students will find it a delight to read
Author: Clement Ampadu
Publisher: Lulu.com
ISBN: 1365109917
Category : Science
Languages : en
Pages : 42
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Book Description
The book is suggested as collateral reading for people interested in "fixed point theorems for contractive type mappings". We continue the investigation of the rth-order Hardy Rogers map in the setting of cone metric spaces. Some open problems in the form of exercises are proposed. The reader comes to grasp with the nitty-gritty ideas of pure mathematical modeling in research. Construction of theorems and proof writing is developed. Researchers in fixed point theory and their students will find it a delight to read
Author: Clement Ampadu_
Publisher: Lulu.com
ISBN: 1365101185
Category : Science
Languages : en
Pages : 43
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Book Description
A research-oriented book focusing on fixed point theorems for contractive type mappings inspired by the Hardy-Rogers Map. Contains many exercises, as the reader begins his or her own investigative inquiry. It is one-of-a-kind research monograph, as the reader gets a taste of how to construct and proof their own theorems.
Author: Clement Ampadu
Publisher: Lulu.com
ISBN: 1365212602
Category : Science
Languages : en
Pages : 47
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Book Description
This book serves as collateral reading for people interested in fixed point theorems for contractive mappings. The higher-order version of the Banach contraction principle is investigated in the setting of multiplicative b-metric space as well as other topics including application to graph theory. The book contains many exercises as the reader begins his or her own investigative inquire into fixed point theorems and related topics. Researchers will find it a delight to read. The exercises hold promise for further research ideas, and can lead to thesis of all sorts including at the postdoctoral level
Author: Clement Ampadu
Publisher: Lulu.com
ISBN: 1365259986
Category : Science
Languages : en
Pages : 46
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Book Description
Serves as collateral reading for people interested in fixed point theorems for contractive type mappings. Researchers in fixed point theory and their students will find it a delight to read. Contains many exercises for further exploration. Construction of theorems and proof writing is developed
Author: Clement Ampadu
Publisher: Lulu.com
ISBN: 1365434745
Category : Science
Languages : en
Pages : 41
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Book Description
Serves as collateral reading for people interested in "stability of iterative sequences for fixed points of contractive type mappings". People with interest in fixed point theory will find it a delight to read. Contains many exercises as the reader begins his or her own investigative inquiry.
Author: Dhananjay Gopal
Publisher: CRC Press
ISBN: 1000366391
Category : Mathematics
Languages : en
Pages : 317
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Book Description
It is an indisputable argument that the formulation of metrics (by Fréchet in the early 1900s) opened a new subject in mathematics called non-linear analysis after the appearance of Banach’s fixed point theorem. Because the underlying space of this theorem is a metric space, the theory that developed following its publication is known as metric fixed point theory. It is well known that metric fixed point theory provides essential tools for solving problems arising in various branches of mathematics and other sciences such as split feasibility problems, variational inequality problems, non-linear optimization problems, equilibrium problems, selection and matching problems, and problems of proving the existence of solutions of integral and differential equations are closely related to fixed point theory. For this reason, many people over the past seventy years have tried to generalize the definition of metric space and corresponding fixed point theory. This trend still continues. A few questions lying at the heart of the theory remain open and there are many unanswered questions regarding the limits to which the theory may be extended. Metric Structures and Fixed Point Theory provides an extensive understanding and the latest updates on the subject. The book not only shows diversified aspects of popular generalizations of metric spaces such as symmetric, b-metric, w-distance, G-metric, modular metric, probabilistic metric, fuzzy metric, graphical metric and corresponding fixed point theory but also motivates work on existing open problems on the subject. Each of the nine chapters—contributed by various authors—contains an Introduction section which summarizes the material needed to read the chapter independently of the others and contains the necessary background, several examples, and comprehensive literature to comprehend the concepts presented therein. This is helpful for those who want to pursue their research career in metric fixed point theory and its related areas. Features Explores the latest research and developments in fixed point theory on the most popular generalizations of metric spaces Description of various generalizations of metric spaces Very new topics on fixed point theory in graphical and modular metric spaces Enriched with examples and open problems This book serves as a reference for scientific investigators who need to analyze a simple and direct presentation of the fundamentals of the theory of metric fixed points. It may also be used as a text book for postgraduate and research students who are trying to derive future research scope in this area.
Author: Richard F. Bass
Publisher:
ISBN: 9781481869140
Category : Mathematical analysis
Languages : en
Pages : 402
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Book Description
This book is a course on real analysis (measure and integration theory plus additional topics) designed for beginning graduate students. Its focus is on helping the student pass a preliminary or qualifying examination for the Ph.D. degree.
Author: Anita Tomar
Publisher:
ISBN: 9781536193367
Category : Fixed point theory
Languages : en
Pages : 0
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Book Description
"Fixed-point theory initially emerged in the article demonstrating existence of solutions of differential equations, which appeared in the second quarter of the 18th century (Joseph Liouville, 1837). Later on, this technique was improved as a method of successive approximations (Charles Emile Picard, 1890) which was extracted and abstracted as a fixed-point theorem in the framework of complete normed space (Stefan Banach, 1922). It ensures presence as well as uniqueness of a fixed point, gives an approximate technique to really locate the fixed point and the a priori and a posteriori estimates for the rate of convergence. It is an essential device in the theory of metric spaces. Subsequently, it is stated that fixed-point theory is initiated by Stefan Banach. Fixed-point theorems give adequate conditions under which there exists a fixed point for a given function and enable us to ensure the existence of a solution of the original problem. In an extensive variety of scientific issues, beginning from different branches of mathematics, the existence of a solution is comparable to the existence of a fixed point for a suitable mapping. The book "Fixed Point Theory & its Applications to Real World Problems" is an endeavour to present results in fixed point theory which are extensions, improvements and generalizations of classical and recent results in this area and touches on distinct research directions within the metric fixed-point theory. It provides new openings for further exploration and makes for an easily accessible source of knowledge. This book is apposite for young researchers who want to pursue their research in fixed-point theory and is the latest in the field, giving new techniques for the existence of a superior fixed point, a fixed point, a near fixed point, a fixed circle, a near fixed interval circle, a fixed disc, a near fixed interval disc, a coincidence point, a common fixed point, a coupled common fixed point, amiable fixed sets, strong coupled fixed points and so on, utilizing minimal conditions. It offers novel applications besides traditional applications which are applicable to real world problems. The book is self-contained and unified which will serve as a reference book to researchers who are in search of novel ideas. It will be a valued addition to the library"--
Author: Christopher J. Bishop
Publisher: Cambridge University Press
ISBN: 1107134110
Category : Mathematics
Languages : en
Pages : 415
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Book Description
A mathematically rigorous introduction to fractals, emphasizing examples and fundamental ideas while minimizing technicalities.
Author: Charalambos D. Aliprantis
Publisher: American Mathematical Soc.
ISBN: 0821841467
Category : Mathematics
Languages : en
Pages : 298
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Book Description
Ordered vector spaces and cones made their debut in mathematics at the beginning of the twentieth century. They were developed in parallel (but from a different perspective) with functional analysis and operator theory. Before the 1950s, ordered vector spaces appeared in the literature in a fragmented way. Their systematic study began around the world after 1950 mainly through the efforts of the Russian, Japanese, German, and Dutch schools. Since cones are being employed to solve optimization problems, the theory of ordered vector spaces is an indispensable tool for solving a variety of applied problems appearing in several diverse areas, such as engineering, econometrics, and the social sciences. For this reason this theory plays a prominent role not only in functional analysis but also in a wide range of applications. This is a book about a modern perspective on cones and ordered vector spaces. It includes material that has not been presented earlier in a monograph or a textbook. With many exercises of varying degrees of difficulty, the book is suitable for graduate courses. Most of the new topics currently discussed in the book have their origins in problems from economics and finance. Therefore, the book will be valuable to any researcher and graduate student who works in mathematics, engineering, economics, finance, and any other field that uses optimization techniques.
