Existence of fixed point theorems in metric spaces G metric spaces and partial metric spaces

Abstract

Fixed point theory is a very extensive and active area of research. It begins with a fixed point and proceeds through the Banach contraction principle. It is a crucial mathematical tool for understanding metric space theory. It assures us about the existence and uniqueness of solutions to various problems across different branches of mathematics. It has found extensive applications in mathematics as well as in other scientific fields also. The existence of a solution to a mathematical or real-world problem is equivalent to the existence of a fixed point for an appropriate map or operator. This concept provides a framework for solving many theoretical and practical problems. In some cases, finding the exact solution is not possible, and in those cases, we have to develop an algorithm to approximate the solution. Fixed point theory acts as the core foundation for approximation algorithms, providing a well-organized framework for addressing complex problems across various fields. This study focuses on fixed-point problems within metric spaces, where distances between points are clearly defined. A significant aspect of this field involves the examination of contraction mappings and distance-related conditions, where a con traction mapping is a function from a metric space to itself that brings points closer together. The current research was completed by dividing it into seven different parts.