Fixed Point Theory in Metric Type Spaces

Fixed Point Theory in Metric Type Spaces

Hardcover(1st ed. 2015)

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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.

Product Details

ISBN-13: 9783319240800
Publisher: Springer International Publishing
Publication date: 03/25/2016
Edition description: 1st ed. 2015
Pages: 385
Product dimensions: 6.10(w) x 9.25(h) x (d)

About the Author

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

Erdal Karapınar
Atılım University
Department of Mathematics
Kızılçaşar Köyü
06836 İncek ANKARA

Donal O’Regan
Department of Mathematics
University of Galway

Antonio F. Roldán-López-de-Hierro
Department of Mathematics
University of Granada

Table of Contents

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 onG-Metric Spaces.- Fixed Point Theorems via Admissible Mappings.- New Approaches to Fixed Point Results onG-Metric Spaces.- Expansive Mappings.- Reconstruction ofG-Metrics:G*-Metrics.- Multidimensional Fixed Point Theorems onG-Metric Spaces.- Recent Motivating Fixed Point Theory.

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