Some results on the fixed point theory in hyperbolic spaces

Hyperbolic spaces, which have convexity properties very similar to linear structures such as normed spaces, have been a productive field of study for fixed point theory. When the relevant literature is examined, it can be seen that many fixed point theorems are obtained by transferring the classical fixed point iteration methods to hyperbolic spaces. This thesis consists of four parts. In the first chapter, literature information about fixed point theory is given. In the second part, the basic concepts of classical analysis and functional analysis are given. In the third chapter, some fixed point iteration methods, and newly defined iteration method are given and some fixed point theorems such as convergence, the equivalence of convergence, convergence speed, and data dependency are obtained by using this method. In the fourth chapter, the results obtained in this study are summarized and possible future studies are given.