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Full Description
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.
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
