Abstract
In this paper, using the concept of attractive points of a nonlinear mapping, we obtain a strong convergence theorem of Halpern’s type [Bull. Amer. Math. Soc. 73 (1967), 957–961] for a wide class of nonlinear mappings which contains nonexpansive mappings, nonspreading mappings and hybrid mappings in a Hilbert space. Using this result, we obtain well-known and new strong convergence theorems of Halpern’s type in a Hilbert space. In particular, we solve a problem posed by Kurokawa and Takahashi [Nonlinear Anal. 73 (2010, 1562–1568].
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Takahashi, W., Wong, NC. & Yao, JC. Attractive points and Halpern-type strong convergence theorems in Hilbert spaces. J. Fixed Point Theory Appl. 17, 301–311 (2015). https://doi.org/10.1007/s11784-013-0142-3
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DOI: https://doi.org/10.1007/s11784-013-0142-3