STRONG CONVERGENCE THEOREMS BY HYBRID METHODS FOR DEMIMETRIC MAPPINGS IN BANACH SPACES

In this paper, using a new nonlinear mapping called demimetric and the C-Q method, we first prove a strong convergence theorem for finding a fixed point for the mapping in a Banach space which generalizes simultaneously the result by Nakajo and Takahashi [11] and the result of Solodov and Svaiter [13] in a Hilbert space. Furthermore, using the mapping and the shrinking projection method, we prove another strong convergence theorem in a Banach space. We apply these results to obtain well-known and new strong convergence theorems in a Hilbert space, or a Banach space.