Duality fixed points for multivalued generalized K_{1}J-pseudocontractive Lipschitzian mappings

Abstract

A generalized class of nonlinear multivalued mappings in uniformly convex Banach spaces is introduced and termed generalized K_{1}J-pseudocontractive mapping. Significantly, this class incorporates various other important classes of pseudocontractive mappings in Banach and Hilbert spaces. A duality fixed point theorem for such generalized class of mappings (assuming that it is also generalized Lipschitzian) is constructed by the modified Ishikawa iterative scheme. Finally, an application to the strictly monotone inclusion problem is also discussed. The obtained theorems extend several known results in the literature.