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 environmentsProvides a unique integration of otherwise disparate domains that aids both students seeking to understand either area and researchers interested in establishing an integrated research approachEmphasizes 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

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