Fixed Point Theory and Its Applications in Engineering Problems

Abstract

The Fixed Point Theory is one of the essential areas of mathematics, which offers solutions to equations, according to which a given function causes a point to be itself. The theory has wide applications in engineering, especially in solving nonlinear equations, optimization, and algorithms that are iterative. To provide solutions with guaranteed existence and uniqueness, fixed point theorems, including the Banach Contraction Principle and the Schauder Fixed Point Theorem provide such assurances, and are usable in the engineering model, where stability and accuracy are needed. Control systems, fluid dynamics, signal processing, structural analysis and electrical circuits are also used in engineering. This paper gives a summary of Fixed Point Theory and explains why it is significant in the solutions of any practical engineering problem based on theoretical and computers techniques.