On Some Applications of Banach Contraction Principle
Project no. 22081 · Status: Kapanmış · 2020
Summary
Fixed point theory has recently become a very popular branch of mathematics, which has attracted the attention of many researchers with its interesting examples and applications to various fields. This theory continues to evolve into three main branches as topological, discrete and metric. Banach fixed point theorem is the most fundamental theorem of the metric fixed point theory. The most important aim of researchers working in this field is to generalize this theorem and apply it to different types of problems to obtain useful results. In this project, some definitions and concepts related to metric fixed point theory are first introduced. Then, detailed information about the $G_b$-metric space and complex valued metric spaces are given. A generalization of Banach contraction principle is proved in complex valued extended $G_b$-metric spaces. Moreover, an application of Banach contraction principle to the solution of Fredholm integral equation is given in this new type metric space. In the last part of the project, it is stated that the objectives of the project are successfully achieved, a significant contribution is made to the literature and some clear problems are included for those who do research on this subject.