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Fixed Point Theory and Graph Theory
Foundations and Integrative Approaches
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
Monther Alfuraidan (Edited by), Qamrul Ansari (Edited by)
9780128042953
Hardback, published 15 June 2016
442 pages
23.4 x 19 x 2.8 cm, 1.06 kg
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.
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
Subject Areas: Discrete mathematics [PBD]
