The purpose of this note is to apply a generalized Kantorovich majorization principle to existence and uniqueness results for Hölder solutions of nonlinear singular integral equations. In contrast to the classical Kantorovich priziciple, we do notrequire differentiability, but only a local Lipschitz condition.
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Jürgen Appell, Antonio Carbone, Petr P. Zabrejko, A Note on the Existence and Uniqueness of Holder Solutions of Nonlinear Singular Integral Equations. Z. Anal. Anwend. 11 (1992), no. 3, pp. 377–384DOI 10.4171/ZAA/599