Fixed Point Theory in Metric Type Spaces

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.

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

Autorentext
Ravi P. Agarwal
Department of Mathematics
Texas A&M University
Kingsville, Texas
USA

Erdal Karapnar
Atlm University
Department of Mathematics
Kzlçaar Köyü
06836 ncek 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

Inhalt
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.