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@article{187673,
        author = {Dr. N. Sreenivasa Reddy and Dr. Pagidi Obulesu},
        title = {Fixed Point Theory - Based Existence and Uniqueness of Solutions to Non-Linear Differential Equations},
        journal = {International Journal of Innovative Research in Technology},
        year = {2025},
        volume = {12},
        number = {6},
        pages = {6208-6213},
        issn = {2349-6002},
        url = {https://ijirt.org/article?manuscript=187673},
        abstract = {Fixed point theory is a branch of mathematics that deals with the study of points where a given function maps a point to itself. The theory has profound implications and applications across various fields of science and engineering. This paper provides an overview of the fundamental concepts in fixed point theory, including important theorems such as Banach’s Fixed Point Theorem, Brouwer’s Fixed Point Theorem, and Schauder’s Fixed Point Theorem. It discusses both the existence and uniqueness of fixed points, the conditions under which they arise, and the methods for finding them through iterative approaches. The paper also explores the wide-ranging applications of fixed-point theory, including optimisation, nonlinear differential equations, game theory, and computational methods. Finally, we discuss the challenges and open problems in this area, especially in relation to high- dimensional and nonlinear systems, as well as the impact of fixed-point theory in various scientific domains. Through this discussion, we aim to highlight both the theoretical importance and practical utility of fixed-point theory in contemporary research.},
        keywords = {},
        month = {November},
        }