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Abstract
This thesis is devoted to study the solutions of some classes of nonlinear singular integral equations and nonlinear singular integral equations with shift where we have studied the following:
Existence of the solutions of a general class of nonlinear singular integral equations with a Carleman shift changing the orientation of first order in the generalized Holder space .
Existence of the solutions of a class of nonlinear singular integral equations with a Carleman shift changing the orientation of first order in the generalized Holder space .
The applicability of the Banach fixed-point theorem to a class of nonlinear singular integral equations with Carleman shift, forming the finite group of iterations, preserving or changing orientation in the generalized Holder space .
The applicability of the Kantorovich majorant method to a class of nonlinear singular integro-differential equations with shift of second order in the generalized Holder space and the obtained results were extended for the case of finite group of iterations. Also the applicability of the generalized Kantorovich majorization principle to a class of nonlinear singular integral equations with shift of finite order in the generalized Holder space .
The applicability of the mechanical quadrature method to a class of nonlinear singular integral equations, with Hilbert kernel, in generalized Hölder spaces.