Existence results for krasnosel'skii type set valued operators

This study consists of ten chapters. In the first chapter, some information was given about the set-valued transformation theory, which is the subject of the thesis. In the second chapter, some studies in the literature related to the subject of the thesis were presented briefly. In the third chapter, the materials and methods used in the thesis were stated. In the fourth chapter, the basic definitions, theorems and lemmas used in the thesis are given. In the fifth chapter, new set-valued versions of Krasnosel'skii type theorems are given under weak topology properties in Banach space. In the sixth chapter, some new existence theorems for set-valued operator equations under weak topology properties in Banach algebra were obtained and the approximation method was used for their proof. In the seventh chapter, some new existence theorems for set-valued operator equations in WC-Banach algebra were obtained and the technique of measure of weak noncompactness was used for their proofs. In the eighth chapter, existence results were obtained for the sum of two set-valued operators under generalized contraction conditions. In the ninth chapter, set-valued transport equations are introduced and existence of the solution for these equations is examined by the Hausdorff measure of non-compactness. Finally, in the tenth chapter, discussion and conclusion regarding the results obtained in this thesis are given.