A nonlinear inclusion problem involving - set-valued mappings in ordered Hilbert space

The purpose of this work is as follows: First, a class of nonlinear inclusion problems involving ( α , λ ) - N O D M set-valued mappings in an ordered Hilbert space is introduced, and then, applying the resolvent operator associated with ( α , λ ) - N O D M set-valued mappings, an existence theorem on the solvability of this class of nonlinear inclusion problems is established. Furthermore, on the basis of the existence theorem and the new ( α , λ ) - N O D M model, a general algorithm is introduced and applied to the approximation solvability of the nonlinear inclusion problem at hand. The results obtained seem to be general in nature.