Strong Convergence Theorems by Hybrid Methods for New Demimetric Mappings in Banach Spaces

Using a new nonlinear mapping called generalized 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 results by Nakajo and Takahashi [12], and Solodov and Svaiter [14] 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 new strong convergence theorems in a Hilbert space and a Banach space.