A KM-BASED ITERATION FOR A SPLIT FEASIBILITY PROBLEM IN HILBERT SPACES

被引：0
作者：
Cho, Sun young [1 ]
Shang, Meijuan [2 ]
机构：
[1] Gyeongsang Natl Univ, Dept Human Hlth Care, Jinju, South Korea
[2] Shijiazhuang Univ, Sch Math, Shijiazhuang, Peoples R China
来源：
JOURNAL OF NONLINEAR FUNCTIONAL ANALYSIS | 2024年 / 2024卷
关键词：
Common fixed point; Monotone operators; Split feasibility problem; Weak convergence; NONEXPANSIVE-MAPPINGS; CONVERGENCE; SETS; THEOREMS;
D O I：
10.23952/jnfa.2024.31
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we investigate a split feasibility problem from the prospective of fixed points. We introduce a KM-based iteration and investigate its convergence. We obtain a weakly convergent theorem of common solutions to the split feasibility problem and a common fixed point problem of an infinite family of nonexpansive mappings in the framework of Hilbert spaces.
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页数：8
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共 22 条
  • [1] Browder F.E., Fixed-point theorems for noncompact mappings in Hilbert space, Proc. Nat. Acad. Sci. USA, 53, pp. 1272-1276, (1965)
  • [2] Browder F.E., Nonexpansive nonlinear operators in a Banach space, Proc. Nat. Acad. Sci. USA, 54, pp. 1041-1044, (1965)
  • [3] Bruck R.E., A common fixed point theorem for a commuting family of nonexpansive mappings, Pacific J. Math, 53, pp. 59-71, (1974)
  • [4] Byrne C., Iterative oblique projection onto convex subsets and the split feasibility problem, Inverse Probl, 18, pp. 441-453, (2002)
  • [5] Censor Y., Elfving T., A multiprojection algorithm using Bregman projections in a product space, Numer. Algo, 8, pp. 221-239, (1994)
  • [6] Censor Y., Bortfeld T., Martin B., Trofimov A., A unified approach for inversion problems in intensitymodulated radiation therapy, Phys. Med. Biol, 51, (2006)
  • [7] Censor Y., Petra S., Schnorr C., Superiorization vs. accelerated convex optimization: The superiorized / regularized least-squares case, J. Appl. Numer. Optim, 2, pp. 15-62, (2020)
  • [8] Censor Y., Elfving T., Kopf N., Bortfeld T., The multiple-sets split feasibility problem and its applications for inverse problems, Inverse Probl, 21, (2005)
  • [9] Chang S.S., Lee H.W.J., Chan C.K., A new method for solving equilibrium problem fixed point problem and variational inequality problem with application to optimization, Nonlinear Anal, 70, pp. 3307-3319, (2009)
  • [10] Dong Q.L., An alternated inertial general splitting method with linearization for the split feasibility problem, Optimmization, 72, pp. 2585-2607, (2023)
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