Fixed Point Theory: A Historical Journey and Its Mathematical Significance

Mehak

doi:10.69968/ijisem.2024v3i463-66

Authors

Mehak M.sc (Mathematics) from S.D college, Ambala cantt

DOI:

https://doi.org/10.69968/ijisem.2024v3i463-66

Keywords:

Fixed point theory, Brouwer, Banach, Schauder, topology, interdisciplinary applications, pure mathematics, applied mathematics

Abstract

Fixed point theory is a significant branch of mathematics with deep roots and extensive applications across various fields, including analysis, topology, game theory, and economics. This paper traces the historical journey of fixed-point theory, beginning with its basic foundations in classical mathematics and progressing to its rigorous formalization in the 20th century. The groundbreaking contributions of mathematicians such as Brouwer, Banach, and Schauder are discussed, highlighting their role in shaping the theory and its application in modern mathematical research. Fixed point theorems, such as Brouwer's Fixed Point Theorem and Banach's Contraction Principle, have become fundamental tools, not only in mathematics but also in solving problems across disciplines. The paper further explores how fixed-point theory acts as a connecting link between pure and applied mathematics. Its interdisciplinary applications in optimization, economic models, and dynamical systems are reviewed. The paper concludes with an overview of current challenges and potential future developments in this field, emphasizing its growing relevance in mathematical and applied research. By presenting a comprehensive analysis, this paper underscores the importance of fixed-point theory as a cornerstone in mathematics.

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