Fixed Point Theory and Graph Theory

Fixed point theorems give the conditions under which maps (single or multivalued) have solutions. FPT is an integration of applied numerical analysis, topology and geometry. They are important because they help to integrate important phenomena in the study of nonlinear phenomena, and have been applied to problems in biology, chemistry, economics, engineering, game theory, and physics. Graph Theory, on the other hand, mathematically structures the relationship between ordered pairs of objects in terms of their vertices and directed edges. Graph theory has been deployed to map many relations and processes across physical, social and information systems, including computer science. Classically, fixed point theory and graph theory are considered as independent subdisciplines of mathematics, but they have mutual applications in different areas of science, engineering, management and social sciences, and important correlations can be discussed between the two. 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. Caristi s fixed point theory is demonstrated in unusual detail. The authors provide solution methods for fixed points in different settings. Two chapters are 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 but common application environmentsUnique attempt to integrate otherwise disparate domains aids both students seeking to understand either area as well as researchers interested in establishing an integrated research directionsThe authors emphasize solution methods for fixed points in non-linear problems such as variational inequalities, split feasibility, and hierarchical variational inequality problems - particularly appropriate for engineering and core science applications. "