Abstract

Using the idea of Halpern iteration, we prove a strong convergence theorem for finding a common fixed point of an infinite family of demimetric mappings in a Hilbert space. Using this result, we obtain well-known and new strong convergence theorems in a Hilbert space.

Author information

Contact details are reproduced from the original publication and may be historical.

Hidetoshi Komiya

Faculty of Business and Commerce, Keio University, Kouhoku-ku, Yokohama 223-8521, Japan

hkomiya@fbc.keio.ac.jp

Wataru Takahashi

Center for Fundamental Science, Kaohsiung Medical University, Kaohsiung 80702, Taiwan
and: Dept. of Mathematical and Computing Sciences, Tokyo Institute of Technology, Ookayama - Meguro-ku, Tokyo 152-8552, Japan

wataru@is.titech.ac.jp

Keywords

  • Common fixed point
  • demimetric mapping
  • metric projection
  • inverse strongly monotone mapping
  • Halpern iteration

Mathematics Subject Classification

47H05, 47H09

Suggested citation

H. Komiya, W. Takahashi. “Strong Convergence Theorems for an Infinite Family of Demimetric Mappings in a Hilbert Space.” Journal of Convex Analysis 24 (2017), No. 4, 1357–1373.

Copyright Heldermann Verlag 2017