Fixed Point Theory and Graph Theory: Foundations and Integrative Approaches

by Monther Alfuraidan, Qamrul Ansari

Overview

Fixed Point Theory and Graph Theory provides an intersection between the theories of fixed point theorems that give the conditions under which maps (single or multivalued) have solutions and graph theory which uses mathematical structures to illustrate the relationship between ordered pairs of objects in terms of their vertices and directed edges.

This edited reference work is perhaps the first to provide a link between the two theories, describing not only their foundational aspects, but also the most recent advances and the fascinating intersection of the domains.

The authors provide solution methods for fixed points in different settings, with two chapters devoted to the solutions method for critically important non-linear problems in engineering, namely, variational inequalities, fixed point, split feasibility, and hierarchical variational inequality problems. The last two chapters are devoted to integrating fixed point theory in spaces with the graph and the use of retractions in the fixed point theory for ordered sets.

Product Details

ISBN-13:	9780128042953
Publisher:	Elsevier Science
Publication date:	06/10/2016
Pages:	442
Product dimensions:	7.50(w) x 9.25(h) x (d)

About the Author

Monther Rashed Alfuraidan is Associate Professor of Mathematics in the Department of Mathematics & Statistics at King Fahd University of Petroleum & Minerals at Dhahran, Saudi Arabia. He obtained his Ph.D. (Mathematics) from Michigan State University. He has written more than twenty articles on graph theory, algebraic graph theory and metric fixed point theory. He peer-reviewed many articles (among others) for: algebraic journal of combinatorics, Arabian Journal of Mathematics, Fixed Point Theory and Applications and Journal of Inequality and Applications.

Qamrul Hasan Ansari is Professor of Mathematics at Aligarh Muslim University, Aligarh, India, and joint professor at King Fahd University of Petroleum \& Minerals, Dhahran, Saudi Arabia. He obtained his Ph.D. (Mathematics) from Aligarh Muslim University, India. He is an associate editor of Journal of Optimization Theory and Applications, Fixed Point Theory and Applications and Carpathian Journal of Mathematics. He also edited several special issues of several journals, namely, Journal of Global Optimization, Fixed Point Theory and Applications, Abstract and Applied Analysis, Journal of Inequalities and Applications, Applicable Analysis, Positivity, Filomat, etc. He has written more than 180 articles on variational inequalities, fixed point theory and applications, vector optimization, etc. in various international peer-reviewed journals. He has edited 6 books for Springer, Taylor & Francis and Narosa, India. He is an author of a book on Metric Spaces published by Narosa, India and has coauthored one book on Variational Inequalities and Nonsmooth Optimization for Taylor & Francis.

Table of Contents

Chapter 1: Caristi-Browder Operator Theory in Distance Spaces

Chapter 2: Iterative Approximation of Fixed Points of Single-valued Almost Contractions

Chapter 3: Approximate Fixed Points

Chapter 4: Viscosity Methods for Some Applied Nonlinear Analysis Problems

Chapter 5: Extragradient Methods for Some Nonlinear Problems

Chapter 6: Iterative Methods for Nonexpansive Type Mappings

Chapter 7: Metric Fixed Point Theory in Spaces with a Graph

Chapter 8: The Use of Retractions in the Fixed Point Theory for Ordered Sets

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From the Publisher

This research monograph synthesizes and uniquely links research advances and applications between the otherwise isolated Metric Fixed Point Theory and Graph Theory domains, highly established theorems in mathematical analysis and discrete mathematics pertinent to applications