Banach Spaces in Linear Differential Equations at Fixed Points and Their Practical Applications

الملخص

This comprehensive study explores the role of Banach spaces and fixed point theory in the analysis of linear differential equations, with a focus on proving the existence and uniqueness of solutions. The research presents a detailed overview of the theoretical foundations of Banach spaces, the properties of linear differential equations, and the principles of fixed point theory. It further provides extensive practical applications of these concepts in diverse fields such as physics, engineering, economics, and biology, illustrating how they can be utilized to understand and predict the behavior of complex real-world systems. The aim is to offer a deep and integrated understanding of these advanced mathematical concepts and their practical implications.