The Existence and uniqueness theorems for nonlinear singular integral equations with Hilbert kernel

In this study, existence and uniqueness for linear and nonlinear singular integral equations with Hubert kernel is examined. First section contains the base concepts and basic knowledge that we have used in our examination. In the first part, metric spaces, norm spaces, the fixed point princible of Banach in metric spaces, the princible of Schauder in norm spaces and a changed form of the mixed point princible of Banach in metric spaces are given. In the second part, the important peculiarities of Hubert kernels singular integral is examined and in princible of this knowledge the existence on uniquness theorems for linear and nonlinear singular integral equations with Hubert kernels are proved. The provided results is applied to the solution of a confirm transformation problem. Theorem 2.2.1, Theorem 2.4.1 which are proved about this subject and its applications in the Theorem of 2.4.7 are orijinal. The key words: Hubert space, Hubert kernels linear and nonlinear singular operators and equations.compact pile, completely continual operator, conform transformation.