Paper Key : IRJ************259
Author: Dr. Kamlesh Kumar Bakariya ,Dr. Krishna Kumar Sen
Date Published: 03 Apr 2025
Abstract
The study of a wide range of equation types that arise in the fields of engineering, biology, physics, and other sciences and technologies has demonstrated the essential importance of fixed point theory. A fixed point of P is a point x of X for which P(x) x for a function P that has a set X as both domain and range. The two basic theorems pertaining to fixed points are the Banach and Brouwer theorems. The distinction between the two main subfields of fixed point theorymetric fixed point theory and topological fixed point theoryis demonstrated by the Banach and Brouwer theorems. Caccioppoli started the systematic application of the Banachs principal to several existence theorems in analysis in 1930. Following that, this principle evolved into a simple instrument for resolving a variety of physics and economics issues. This principle has since been expanded and extended to a variety of metric and generalized metric spaces.