Published Paper Details:

Fixed point theorems and contraction mappings are essential components of mathematical analysis with significant theoretical and practical applications. This study delves into the fundamental concepts of fixed points and contraction mappings, exploring their mathematical properties, proof techniques, and diverse applications. We begin with a comprehensive review of classical fixed point theorems, including the Banach, Brouwer, and Schauder theorems, highlighting their unique properties and implications. The theoretical analysis is complemented by rigorous proofs and the formulation of new theorems that extend existing results to broader contexts. Our methodology includes the development of iterative algorithms based on contraction mappings, which are implemented and tested through computational experiments. We perform convergence and error analysis to evaluate the efficiency and robustness of these algorithms. Practical applications are explored in various fields such as differential equations, optimization, economics, and computer science, demonstrating the versatility and utility of fixed point theorems. The data analysis phase involves both theoretical exploration and computational validation, using statistical and graphical methods to interpret the results. Case studies on solving differential equations and optimization problems illustrate the practical impact of fixed point methods. The findings are documented and presented through detailed visualizations and comparative analyses, providing a clear understanding of the efficiency and applicability of the developed algorithms. This study not only advances the theoretical framework of fixed point theorems and contraction mappings but also provides powerful tools for solving real-world problems, emphasizing the importance of these concepts in both mathematical research and practical applications.