Some periodic point results on partial metric spaces

Fixed point theory is an exciting area of research in metric spaces that began at the beginning of the twentieth century. Fixed-point theorems are mainly useful when dealing with problems that arise in the theory of existence of differential equations, integral equations, partial differential equations, dynamic programming, fractal modeling, chaos theory, and various other disciplines of mathematics, statistics, engineering, and economics, approximation theory. For this reason, fixed point studies have been studied in many different metric spaces. In this sense, Matthews (1994) defined partial metric spaces as a generalization of metric spaces and studied fixed point theorems. On the other hand, Ciri ´ c (1974) introduced the concept of periodic point, which is a ´ generalization of the fixed point. This thesis consists of four parts. In the first chapter, basic definitions and theorems that will be used throughout the thesis are given. In the second part, the main result of Karapinar (2012) is examined in detail. The third chapter is the original part of the thesis. In this section, some periodic point results are obtained with the help of Boyd-Wong and Bianchini-Grandolfi gauge functions. In the last section, discussion and conclusion are given. 2021, 40 pages Keywords: Partial metric space, fixed point, periodic point