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.
Rezensionen / Stimmen
"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." (Jaroslaw 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. Cobzas, Studia Universitatis Babes-Bolyai, Mathematica, Vol. 61 (3), 2016)
Auflage
Softcover reprint of the original 1st ed. 2015
Sprache
Verlagsort
Verlagsgruppe
Springer International Publishing
Zielgruppe
Illustrationen
Maße
Höhe: 235 mm
Breite: 155 mm
Dicke: 22 mm
Gewicht
ISBN-13
978-3-319-79576-8 (9783319795768)
DOI
10.1007/978-3-319-24082-4
Schweitzer Klassifikation
Ravi P. Agarwal
Department of Mathematics
Texas A&M University
Kingsville, Texas
USA
Erdal Karapınar
Atılım University
Department of Mathematics
Kızılçasar Köyü
06836 Incek 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
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.
