• Bulletin of the Korean Mathematical Society
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• v.40 no.3
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• pp.351-363
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• 2003

In the present paper, some general convergence principles are established in metric spaces and then theses principles are applied to the convergence of the iterative sequences for approximating fixed points of certain classes of mappings. By virtue of our principles, most of the latest results obtained by several authors can be deduced easily.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.38 no.4
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• pp.11-19
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• 2001

In this paper, we study the convergence property of iterative learning control (ILC). First, we present a new method to prove the convergence of ILC using sup-norm. Then, we propose a new type of ILC algorithm adopting intervalized learning scheme and show that the monotone convergence of the output error can be obtained for a given time interval when the proposed ILC algorithm is applied to a class of linear dynamic systems. We also show that the divided time interval is affected from the learning gain and that convergence speed of the proposed learning scheme can be increased by choosing the appropriate learning gain. To show the effectiveness of the proposed algorithm, two numerical examples are given.

• Nonlinear Functional Analysis and Applications
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• v.29 no.3
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• pp.673-710
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• 2024

In this paper, we propose a modified Halpern's iterative scheme developed from a sequence of a new class of enriched nonspreading mappings and an enriched nonexpansive mapping in the setup of a real Hilbert space. Moreover, we prove strong convergence theorem of the proposed method under mild conditions on the control parameters. Also, we obtain some basic properties of our new class of enriched nonspreading mappings.