Banach contraction principle and applications

This thesis thoroughly examines the Banach Fixed Point Theorem and its associated applications. The Banach Fixed Point Theorem is a significant tool in the theory of metric spaces. This theorem has wide-ranging application potential in mathematical analysis and various scientific fields. It guarantees the existence and determination of fixed points for functions that meet specific conditions. The theorem was first formulated by Stefan Banach in 1922. The thesis provides a detailed exposition of the fundamental principles of the Banach Fixed Point Theorem and subsequently explores generalizations and applications in various mathematical domains and other fields such as economics and engineering. Examples of applications include differential and integral equations, Cauchy problems, among others. Lastly, the thesis caters to a broad audience, ranging from mathematicians seeking to understand the theoretical foundations of the Banach Fixed Point Theorem to scientists interested in exploring its practical applications. The goal of the thesis is to provide an in-depth understanding of the Banach Fixed Point Theorem and to unveil the mathematical and practical dimensions of its various applications.