Overview
Written by the leading experts in the field of fixed point theory and metric type spaces
Presents a self-contained account of the theory, techniques, and results in the rapidly-growing field of metric type spaces, while demonstrating connections to pure and applied mathematics
Guides the reader through the preliminary stages with historical notes on metric spaces, before moving to a discussion of Banach type contraction theorems and fixed point theory in metric type spaces, and concluding with generalizations and the latest results
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Table of contents (12 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.
Reviews
“This book is basically a compendium of various results concerning fixed points of mappings on different metric-type spaces studied by authors in the last few decades. … The book will be useful to anyone who wishes to write a thesis on some aspect of fixed point theory in spaces … .” (S. Swaminathan, Mathematical Reviews, December, 2016)
“This self-contained book provides the first systematic presentation of fixed point theory in G-metric spaces … . Most of the results presented here were obtained by the authors over the last years and have not previously appeared in any other textbook. This book is mainly addressed to graduate students who wish to learn about fixed point theory in metric type spaces and researchers working in nonlinear functional analysis.” (Jarosław Górnicki, zbMATH 1347.54001, 2016)
“The book, including many contributions of its authors, provides an accessible and up-to-date source of information for researchers in fixed point theory in metric spaces and in various of their generalizations, for mappings satisfying some very general conditions.” (S. Cobzaş, Studia Universitatis Babes-Bolyai, Mathematica, Vol. 61 (3), 2016)
Authors and Affiliations
About the authors
Department of Mathematics
Texas A&M University
Kingsville, Texas
USA
Erdal Karapınar
Atılım University
Department of Mathematics
Kızılçaşar Köyü
06836 İncek ANKARA
Turkey
Donal O’Regan
Department of Mathematics
University of Galway
Galway
Ireland
Antonio F. Roldán-López-de-Hierro
Department of Mathematics
University of Granada
Granada
Bibliographic Information
Book Title: Fixed Point Theory in Metric Type Spaces
Authors: Ravi P. Agarwal, Erdal Karapınar, Donal O’Regan, Antonio Francisco Roldán-López-de-Hierro
DOI: https://doi.org/10.1007/978-3-319-24082-4
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2015
Hardcover ISBN: 978-3-319-24080-0Published: 04 April 2016
Softcover ISBN: 978-3-319-79576-8Published: 19 April 2018
eBook ISBN: 978-3-319-24082-4Published: 24 March 2016
Edition Number: 1
Number of Pages: XVII, 385
Topics: Numerical Analysis, Real Functions, Functional Analysis