The utilization of Bernstein polynomials in constructing and numerically integrating bivariate fractal interpolation functions is a prominent research focus. It involves the construction and numerical integration of these functions over various domains. Furthermore, a significant aspect of this field pertains to the fixed-point results derived for the sum of two operators and their application in solving differential equations. In a related context, the existence and uniqueness of a coupled best attractor for proximal Iterated Function Systems (IFS) are explored. This concept plays a fundamental role in understanding the behavior of fractal interpolations. Additionally, the investigation into the existence of common best proximity points within a topological space is a crucial topic. This endeavor aims to establish foundational principles and theorems in mathematical analysis and functional analysis, enhancing our understanding of these intricate mathematical concepts.