Abstract. A generalized class of nonlinear multivalued mappings in uniformly
convex Banach spaces is introduced and termed generalized K1J-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.