%0 Journal Article
%T 利用Fejér单调性的两个算子和的收敛性定理<br>Convergence Theorem for the Sum of Two Operators via Fejér Monotonicity
%A 洪嘉聪
%J Pure Mathematics
%P 1-8
%@ 2160-7605
%D 2024
%I Hans Publishing
%R 10.12677/PM.2024.141001
%X 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。<br />
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.
%K 预解式，Fejér单调性，包含问题，强收敛，弱收敛<br>Resolvent
%K Fejér Monotonicity
%K Inclusion Problems
%K Strong Convergence
%K Weak Convergence
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=79048