Strong convergence theorem by shrinking projection method for new nonlinear mappings in Banach spaces and applications |
| |
| Authors: | Wataru Takahashi Ching-Feng Wen |
| |
| Institution: | 1. Center for Fundamental Science, Kaohsiung Medical University, Kaohsiung, Taiwan.;2. Keio Research and Education Center for Natural Sciences, Keio University, Kouhoku-ku, Yokohama, Japan.;3. Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Tokyo, Japan. |
| |
| Abstract: | In this paper, we introduce the concept of a new nonlinear mapping called demigeneralized in a Banach space. Then, using the shrinking projection method, we prove a strong convergence theorem for finding a common fixed point for a family of the new nonlinear mappings in a Banach space. We apply this result to obtain new strong convergence theorems in a Hilbert space and a Banach space, respectively. |
| |
| Keywords: | Fixed point generalized projection generalized resolvent shrinking projection method duality mappinng |
|
|
