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Pure Mathematics 2024
利用Fejér单调性的两个算子和的收敛性定理
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Abstract:
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。
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.
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