Attractive points and Halpern-type strong convergence theorems in Hilbert spaces

作者：Takahashi, Wataru^*; Wong, Ngai Ching; Yao, Jen Chih

来源：Journal of Fixed Point Theory and Applications, 2015, 17(2): 301-311.

DOI：10.1007/s11784-013-0142-3

• Attractive point
• fixed point
• generalized hybrid mapping
• Halpern-type iteration
• nonexpansive mapping

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].

• 出版日期2015-6
• 单位中山大学