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

被引：0
|
作者：
Wataru Takahashi
Ngai-Ching Wong
Jen-Chih Yao
机构：
[1] National Sun Yat-sen University,Department of Applied Mathematics
[2] Tokyo Institute of Technology,Department of Mathematical and Computing Sciences
[3] Kaohsiung Medical University,Center for Fundamental Science
来源：
Journal of Fixed Point Theory and Applications | 2015年 / 17卷
关键词：
47H10; 47H05; 47H09; Attractive point; fixed point; generalized hybrid mapping; Halpern-type iteration; nonexpansive mapping;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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].
引用
收藏
页码：301 / 311
页数：10
相关论文
共 50 条
  • [1] Attractive points and Halpern-type strong convergence theorems in Hilbert spaces
    Takahashi, Wataru
    Wong, Ngai-Ching
    Yao, Jen-Chih
    [J]. JOURNAL OF FIXED POINT THEORY AND APPLICATIONS, 2015, 17 (02) : 301 - 311
  • [2] THE SPLIT COMMON NULL POINT PROBLEM AND HALPERN-TYPE STRONG CONVERGENCE THEOREM IN HILBERT SPACES
    Alofi, A. S.
    Alsulami, Saud M.
    Takahashi, W.
    [J]. JOURNAL OF NONLINEAR AND CONVEX ANALYSIS, 2015, 16 (05) : 775 - 789
  • [3] TWO GENERALIZED STRONG CONVERGENCE THEOREMS OF HALPERN'S TYPE IN HILBERT SPACES AND APPLICATIONS
    Takahashi, Wataru
    Wong, Ngai-Ching
    Yao, Jen-Chih
    [J]. TAIWANESE JOURNAL OF MATHEMATICS, 2012, 16 (03): : 1151 - 1172
  • [4] HALPERN-TYPE STRONG CONVERGENCE THEOREM FOR WIDELY MORE GENERALIZED HYBRID MAPPINGS IN HILBERT SPACES AND APPLICATIONS
    Hojo, Mayumi
    Takahashi, Wataru
    [J]. JOURNAL OF NONLINEAR AND CONVEX ANALYSIS, 2015, 16 (09) : 1761 - 1771
  • [5] Strong Convergence Theorems of Halpern's Type for Families of Nonexpansive Mappings in Hilbert Spaces
    Nakajo, K.
    Shimoji, K.
    Takahashi, W.
    [J]. THAI JOURNAL OF MATHEMATICS, 2009, 7 (01): : 49 - 67
  • [6] On the strong convergence of sequences of Halpern type in Hilbert spaces
    Jaipranop, Ch.
    Saejung, S.
    [J]. OPTIMIZATION, 2018, 67 (11) : 1895 - 1922
  • [7] Strong convergence of the Modified Halpern-type iterative algorithms in Banach spaces
    Cho, Yeol Je
    Qin, Xiaolong
    Kang, Shin Min
    [J]. ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA, 2009, 17 (01): : 51 - 68
  • [8] STRONG CONVERGENCE THEOREMS FOR COMMON ATTRACTIVE POINTS OF WIDELY MORE GENERALIZED HYBRID MAPPINGS IN HILBERT SPACES
    Thongpaen, Panadda
    Suantai, Suthep
    Inthakon, Warunun
    [J]. JOURNAL OF NONLINEAR AND CONVEX ANALYSIS, 2021, 22 (04) : 715 - 722
  • [9] A sufficient and necessary condition for Halpern-type strong convergence to fixed points of nonexpansive mappings
    Suzuki, Tomonari
    [J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2007, 135 (01) : 99 - 106
  • [10] Strong convergence of a Halpern-type iteration algorithm for fixed point problems in Banach spaces
    Yao, Zhangsong
    Zhu, Li-Jun
    Liou, Yeong-Cheng
    [J]. JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS, 2015, 8 (05): : 489 - 495
12345