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.
Publisher: Springer International Publishing AG
Number of pages: 385
Weight: 7273 g
Dimensions: 235 x 155 x 24 mm
Edition: 1st ed. 2015
"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 Gornicki, 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)