Название: An in-Depth Guide to Fixed-Point Theorems
Автор: Rajinder Sharma, Vishal Gupta
Издательство: Nova Science Pub Inc
Год: 2021
Страниц: 268
Язык: английский
Формат: pdf (true)
Размер: 23.8 MB

This book details fixed point theory, a gripping and wide-ranging field with applications in multifold areas of pure and applied mathematics. The content comprises both theoretical and practical applications. The evolution of the main theorems on the existence and uniqueness of fixed points of maps are presented. Applications covering topological properties, a nonlinear stochastic integral equation of the Hammerstein type, the existence and uniqueness of a common solution of the system of Urysohn integral equations, and the existence of a unique solution for linear equations system are included in this selection.

Fixed point theory is an attractive area of Functional Analysis. Several major branches of Mathematics and Engineering including set theory, general topology, algebraic topology, robotic analysis provides natural setting for fixed point theorems. An application of fixed-point theorems encompasses diverse disciplines of mathematics, statistics, engineering, biology, and economics. Using fixed point theory techniques, it is possible to analyze several concrete problems from science and engineering, where one is concerned with a system of differential/integral/functional equations. This approach is also useful in dealing with certain problems of control systems and theory of elasticity. Fixed Point theorems are the most important tools for proving the existence and the uniqueness of the solutions to various mathematical models (differential, integral, PDE and variational inequalities etc.) representing phenomena arising in the different fields such as steady state temperature distribution, chemical reactions, neuron transport theories, economic theories, epidemic and flow of fluids. Fixed point Theory also provide mathematical basis to carry out asymptotic complexity analysis of algorithms.