Fixed Point Theory in Metric Type Spaces

Ravi P. Agarwal Department of Mathematics Texas A&M University Kingsville, Texas USA Erdal Karapinar Atilim University Department of Mathematics Kizilçasar 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.

"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)