Fixed Point Theory and Graph Theory: Foundations and Integrative Approaches

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.

• Introduces both metric fixed point and graph theory in terms of their disparate foundations and common application environments
• Provides a unique integration of otherwise disparate domains that aids both students seeking to understand either area and researchers interested in establishing an integrated research approach
• Emphasizes solution methods for fixed points in non-linear problems such as variational inequalities, split feasibility, and hierarchical variational inequality problems that is particularly appropriate for engineering and core science applications

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.