Split Common Null Point and Common Fixed Point Problems Between Banach Spaces and Hilbert Spaces

In this paper, we present a new algorithm for solving the split common null point and the common fixed point problems between Banach spaces and Hilbert spaces, to find a point which belongs to the common zero point set of a finite family of maximal monotone operators and the common fixed point set of a finite family of demicontractive mappings in a Hilbert space such that its image under a linear transformation belongs to the common zero point set of another finite family of maximal monotone operators in a Banach space. We prove that the sequence generated by the proposed algorithm converges strongly to a common solution of the split common null point and the common fixed point problems, which is also an unique solution of a variational inequality as an optimality condition for a minimization problem.