Abstract
Our main aim in the present paper is the search for a zero of the sum of a single-valued differentiable function and a multivalued Hausdorff-continuous function. Our approach is constructive and replaces the given problem with an infinite collection of Newton-type approximate problems whose solutions converge to the desired solution. Our class of approximate problems is quite wide and contains as special cases many generalized Newton-type schemes that have been studied by Argyros, Zabrejko, Nguen, Uko and other authors.
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