Fixed point results for multivalued mappings on geodesic spaces

In this thesis, it has been studied in geodesic spaces, on the problems of the existence of fixed points and convergence to fixed points of new defined multivalued mappings together with multivalued generalizations of some single valued mappings. This thesis consists of six sections. In the first section, the review of literature, the aim of the thesis and hypothesis are given. In the second section, the basic concepts, definitions and theorems which will be used throughout the thesis are presented. In the third section, nonexpansive-like multivalued hybrid mappings are introduced and along with existence of fixed points and some convergence to fixed points, it has been shown that fixed points sets of these mapping classes are stable. In the fourth section, contraction-like multivalued hybrid mappings are introduced and along with existence of fixed points and some convergence to fixed points, it has been shown that fixed points sets of these mapping classes are stable. Additionally, it has been shown that the iteration methods which converging to the fixed points are T-stable. In the fifth section, various convergences have been studied for the common fixed points of finite family of nonexpansive mappings. In the last section, the results obtained in this thesis are summarized and possible studies that can be done in the future are stated.