Metric Structures and Fixed Point Theory

It is an indisputable argument that the formulation of metric (by Frechet in early 1900's) opens a new subject in mathematics called non-linear analysis after the appearance of Banach fixed point theorem. Because the underlined space of this theorem is a metric space, the theory that developed following its publications is known as the metric fixed point theory. It is well known that metric fixed point theory provides essential tools for solving problems arising in various branches of mathematics and other sciences such as Split feasibility problems, variational inequality problems, nonlinear optimization problems, equilibrium problems, selection and matching problems, and problems of proving an existence of solution of integral and differential equations are closely related with fixed point theory. Due to this reason over the last seventy years many people have tried to generalize the definition of metric space and corresponding fixed point theory and this trend is still going on. A few questions lying at the heart of the theory remain open and there are many unanswered questions regarding the limits to which the theory may be extended.Metric Structures and Fixed Point Theory provides an extensive understanding and latest updates on the subject. The book decomposed into nine chapters not only shows diversified aspects on popular generalizations of metric spaces such as symmetric, b-metric, w-distances, G-metric, modular metric, probabilistic metric, fuzzy metric, graphical metric and corresponding fixed point theory but also motivate to work on existing open problems on the subject . Each chapter contributed by different authors contains a section Introduction which summarizes the material needed to read the chapter independent of others and contains a necessary background, several examples, and comprehensive literature to comprehend the concepts presented therein. This could be helpful for those who want to pursue their research career in metric fixed point theory and its related areas. Features: · Explore the latest research and developments in fixed point theory on the most popular generalizations of metric spaces. · Description on various generalizations of metric spaces. · A very new topics on fixed point theory in graphical and modular metric spaces.· Enrich with examples and open problems. This book serves as a reference book for scientific investigators who need to analyze a simple and direct presentation of the fundamentals of the theory of metric fixed point. It may also be used as a text book for post graduate and research students who try to derive future research scope in this area.