الفهرس 
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Abstract
In the thesis we prove the boundedness of a discrete singular operator in the generalized HÕlder space and we solve a nonlinear singular integral equation with Hilbert Kernel in the generalized HÕlder space . Also we solve the same equation by the method of mechanical quadrature in the space . We discuss the sufficient conditions of the applicability and convergence of Newton-Kantorovich method to another nonlinear integral equation in the space