Geometric approach to fixed point theory in elliptic valued metric spaces

In this thesis, firstly, some examples of elliptic valued metric spaces are given. Later, circles are introduced in elliptic valued metric spaces and fixed circles are investigated in these spaces. Finally, the existence and uniqueness of fixed circles in elliptic valued metric spaces are shown. This study consists of seven chapters. The first chapter is devoted to the introduction, and in this chapter, a brief literature review for fixed point theory is given. In addition, fixed circle and elliptic metric spaces are also mentioned. In the second part, definitions and theorems are given under the umbrella of basic concepts about the subject. In the third chapter, some examples of these spaces are given in order to study elliptic valued metric spaces better. In the third chapter, some examples of the elliptic valued metric spaces are given in order to study these spaces better. In the fifth chapter, theorems about the conditions under which fixed circles can be obtained in elliptic valued metric spaces are given, and these theorems are exemplified by some transformation examples with or without fixed circles. In the sixth chapter, the uniqueness conditions of fixed circles in elliptic valued metric spaces are examined. Finally, in the seventh chapter, the results obtained from this thesis and the studies that can be done in the light of these results are mentioned.