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Fixed point theory in metric type spaces

✍ Scribed by Agarwal, Ravi P.; Karapınar, Erdal; O'Regan, Donal; Roldán López de Hierro, Antonio Francisco

Publisher
Springer
Year
2015
Tongue
English
Leaves
395
Category
Library
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✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xvii
Introduction with a Brief Historical Survey....Pages 1-4
Preliminaries....Pages 5-31
G-Metric Spaces....Pages 33-50
Basic Fixed Point Results in the Setting of G-Metric Spaces....Pages 51-78
Fixed Point Theorems in Partially Ordered G-Metric Spaces....Pages 79-105
Further Fixed Point Results on G-Metric Spaces....Pages 107-173
Fixed Point Theorems via Admissible Mappings....Pages 175-198
New Approaches to Fixed Point Results on G-Metric Spaces....Pages 199-217
Expansive Mappings....Pages 219-227
Reconstruction of G-Metrics: G ∗-Metrics....Pages 229-248
Multidimensional Fixed Point Theorems on G-Metric Spaces....Pages 249-361
Recent Motivating Fixed Point Theory....Pages 363-367
Back Matter....Pages 369-385

✦ Subjects

Fixed point theory;MATHEMATICS / Calculus;MATHEMATICS / Mathematical Analysis

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