利用Fejér单调性的两个算子和的收敛性定理
Convergence Theorem for the Sum of Two Operators via Fejér Monotonicity
DOI: 10.12677/PM.2024.141001, PDF,   
作者: 洪嘉聪：云南财经大学统计与数学学院，云南 昆明
关键词: 预解式；Fejér单调性；包含问题；强收敛；弱收敛；Resolvent； Fejér Monotonicity； Inclusion Problems； Strong Convergence； Weak Convergence
摘要: 本文研究了实Hilbert空间中的一类变分包含问题，并给出了该问题解的一个充要条件。通过利用Fejér单调性证明了在给定条件下迭代序列的弱收敛性，以及阴影序列的强收敛性，同时我们得到了该阴影序列强收敛到原变分包含问题的解。
Abstract: In this paper, we study a class of variational inclusion problem in real Hilbert space and give a necessary and sufficient condition for the solution of this problem. Via the Fejér monotonicity, we prove weak convergence of the iterative sequences and strong convergence of the shadow se-quences under given conditions. Moreover, we get that the shadow sequences converge strongly to the solution of the original variational inclusion problem.
文章引用：洪嘉聪. 利用Fejér单调性的两个算子和的收敛性定理[J]. 理论数学, 2024, 14(1): 1-8. https://doi.org/10.12677/PM.2024.141001

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