On Some Generalizations of Banach Contraction Principle
Project no. 22082 · Status: Kapanmış · 2020
Summary
Metric fixed point theory has recently become an important field with applications in many fields such as medicine, biology, physics, chemistry and engineering, as well as mathematics. Banach contraction principle is central to this project work. Generalization of this theorem, which is a fundamental tool for solving differential equations and integral equations in the field of mathematics, can provide answers to many types of problems. In this project, some basic definitions and concepts related to metric fixed point theory are first introduced. Detailed information is given on $b_v(s)$-metric space, complex valued metric space and complex C-class function that form the basis of the project. The concept of complex valued $b_v(s)$-metric space is introduced for the first time and brought to the literature. Then, a generalization of the Reich fixed point theorem, which is a generalization of the Banach contraction principle, in complex valued $b_v(s)$-metric spaces is discussed and proved. Moreover, a generalization of Banach contraction principle is expressed and proved by means of the complex C-class function in the same 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.