About Applications of the Fixed Point Theory

Abstract

The fixed point theory is essential to various theoretical and applied fields, such as variational and linear inequalities, the approximation theory, nonlinear analysis, integral and differential equations and inclusions, the dynamic systems theory, mathematics of fractals, mathematical economics (game theory, equilibrium problems, and optimisation problems) and mathematical modelling. This paper presents a few benchmarks regarding the applications of the fixed point theory. This paper also debates if the results of the fixed point theory can be applied to the mathematical modelling of quality.

A New Extension of CJ Metric Spaces—Partially Controlled J Metric Spaces

“…This fixed theory has many applications in economics, such as game theory, for finding equilibrium points and optimization problems [9]. It is very interesting and useful in the existence of orbits and the study of dynamical systems [9].…”

“…This fixed theory has many applications in economics, such as game theory, for finding equilibrium points and optimization problems [9]. It is very interesting and useful in the existence of orbits and the study of dynamical systems [9]. Moreover, in mathematics, it has significant applications, especially in solving nonlinear hybrid differential equations [10,11], and it is also used to solve some nontrivial equations [12], which has motivated researchers to work further on the fixed point theory.…”

A Special Mutation Operator in the Genetic Algorithm for Fixed Point Problems

“…The fixed point theory was introduced scientifically in the 20th century. The basis of this theory is the principle of the Picard-Banach-Caccioppoli, which led to important lines of research and applications of this theory [1]. Fixed point theory is used and is important in various theoretical and practical fields.…”

Positive fixed points of quadratic operators and Gibbs measures

“…It is well known that fixed point theory is a very important tool for solving problems in Nonlinear Functional Analysis and as well as to various theoretical and applied fields such as variational and linear inequalities, the dynamic systems theory, nonlinear analysis [8]. Nonlinear operators are connected with problems in statistical physics, biology, thermodynamics, statistical mechanics and so on [5], [9], [10].…”