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Journal of Convex Analysis 24 (2017), No. 4, 1357--1373
Copyright Heldermann Verlag 2017

Strong Convergence Theorems for an Infinite Family of Demimetric Mappings in a Hilbert Space

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

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

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.

Keywords: Common fixed point, demimetric mapping, metric projection, inverse strongly monotone mapping, Halpern iteration.

MSC: 47H05, 47H09

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