A NOTE ON THE SOLUTION OF A NONLINEAR SINGULAR INTEGRAL EQUATION WITH A SHIFT IN GENERALIZED $H{\ddot{O}}LDER$ SPACE

Using the center instead of the Lipschitz condition we show how to provide weaker sufficient convergence conditions of the modified Newton Kantorovich method for the solution of nonlinear singular integral equations with Curleman shift (NLSIES). Finer error bounds on the distances involved and a more precise information on the location of the solution are also obtained and under the same computational cost than in [1].