On fixed points of F-contraction mappings on B-metric space

Since the beginning of the 20th century, the study of fixed points in metric spaces has been an attractive field of study. Fixed-point theorems are useful when dealing with problems that arise mainly in the theory of existence of differential equations, integral equations, partial differential equations, dynamic programming, fractal modeling, chaos theory, economics, theory of approximation, and various other mathematics, statistics, engineering, and other disciplines. For this reason, fixed point studies have been studied in many different metric spaces. In this thesis, some results obtained with the help of Ď- contraction in the literature are examined in detail. This thesis contains three chapters. In the first chapter, we present the motivation of the thesis and some information related to fixed point theory are given. In the second chapter, we recall the definitions of metric and 𝑏-metric space, and their properties. Also, we give some concepts, definitions and theorems about the fixed point theory. In the third chapter, we will examine some results obtained by the Ď-contraction existing in the literature.