A strong convergence theorem for countable families of nonlinear nonself mappings in Hilbert spaces and applications (Study on Nonlinear Analysis and Convex Analysis)

In [17] Takahashi introduced the concept of demimetric mappings in Banach spaces and Alsulami and Takahashi [2] showed strong convergence theorems for demimetric mappings in Hilbert spaces. On the other hand, in [7] Kawasaki and Takahashi introduced the concept of widely more generalize hybrid mappings in Hilbert spaces. Such a mapping is not demimetric generally even if the set of fixed points of the mapping is nonempty. In this paper, we extend the class of demimetric mappings to a more broad class of mappings in Banach spaces and prove a strong convergence theorem applicable to the class of widely more generalized hybrid mappings in a Hilbert space. Using this result, we obtain strong convergence theorems which are connected to the class of widely more generalized hybrid mappings in a Hilbert spaces