Fixed Point Theory in Metric Type Spaces

Ravi P. Agarwal, Erdal KARAPINAR, Donal O’Regan , Antonio Francisco Roldán-López-de-Hierro

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English

Springer International Publishing AG
19 April 2018

Number systems; Calculus & mathematical analysis; Calculus; Functional analysis & transforms

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.

By: Ravi P. Agarwal, Erdal KARAPINAR, Donal O’Regan, Antonio Francisco Roldán-López-de-Hierro
Imprint: Springer International Publishing AG
Country of Publication: Switzerland
Edition: Softcover reprint of the original 1st ed. 2015
Dimensions: Height: 235mm, Width: 155mm, Spine: 21mm
Weight: 6.088kg
ISBN: 9783319795768
ISBN 10: 3319795767
Pages: 385
Publication Date: 19 April 2018
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

Introduction with a Brief Historical Survey.- Preliminaries.- G-Metric Spaces.- Basic Fixed Point Results in the Setting of G-Metric Spaces.- Fixed Point Theorems in Partially Ordered G-Metric Spaces.- Further Fixed Point Results on G-Metric Spaces.- Fixed Point Theorems via Admissible Mappings.- New Approaches to Fixed Point Results on G-Metric Spaces.- Expansive Mappings.- Reconstruction of G-Metrics: G*-Metrics.- Multidimensional Fixed Point Theorems on G-Metric Spaces.- Recent Motivating Fixed Point Theory.

Ravi P. Agarwal 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

Reviews for Fixed Point Theory in Metric Type Spaces

“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)