Metric Structures and Fixed Point Theory

Name: Metric Structures and Fixed Point Theory
Brand: CRC Press

CRC Press

It is an indisputable argument that the formulation of metrics (by Fr\u00E9chet in the early 1900s) opened a new subject in mathematics called non-linear analysis after the appearance of Banach\u2019s fixed point theorem. Because the underlying space of this theorem is a metric space, the theory that developed following its publication is known as 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, non-linear optimization problems, equilibrium problems, selection and matching problems, and problems of proving the existence of solutions of integral and differential equations are closely related to fixed point theory. For this reason, many people over the past seventy years have tried to generalize the definition of metric space and corresponding fixed point theory. This trend still contin.