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Abstract
This thesis is devoted to study the solutions of some classes of nonlinear
singular integral equations with Cauchy and Hilbert kernel where we have studied the following:
The existence theorem of the solution of some classes of nonlinear singular integral equations with Hilbert kernel in Sobolev spaces [ ].
The sufficient conditions and applicability of Kantorovich majorant method to a certain class of nonlinear singular integral equations with Hilbert kernel in the usual Hölder spaces
The existence and uniqueness of solutions of certain class of nonlinear singular integral equations in generalized Hölder space by means of Schauder fixed point theorem and Banach fixed point theorem.