To our knowledge it is not known whether a strong convergence theorem of Halpern's type for nonspreading mappings holds or not, even in Hilbert space. In this paper we obtain some partial positive answers, that are meaningful in the context of variational inequalities, by using ergodic type theorems.
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Tokyo Inst Technol, Dept Math & Comp Sci, Tokyo 1528552, JapanTokyo Inst Technol, Dept Math & Comp Sci, Tokyo 1528552, Japan
Kurokawa, Yu
Takahashi, Wataru
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Tokyo Inst Technol, Dept Math & Comp Sci, Tokyo 1528552, Japan
Natl Sun Yat Sen Univ, Kaohsiung, TaiwanTokyo Inst Technol, Dept Math & Comp Sci, Tokyo 1528552, Japan