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Mathematics 2019, 7(3), 215; https://doi.org/10.3390/math7030215

Extension and Application of the Yamada Iteration Algorithm in Hilbert Spaces

1
College of Science, Civil Aviation University of China, Tianjin 300300, China
2
Tianjin Key Laboratory for Advanced Signal Processing, Civil Aviation University of China, Tianjin 300300, China
*
Author to whom correspondence should be addressed.
Received: 17 January 2019 / Revised: 19 February 2019 / Accepted: 20 February 2019 / Published: 26 February 2019
(This article belongs to the Special Issue Fixed Point, Optimization, and Applications)
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Abstract

In this paper, based on the Yamada iteration, we propose an iteration algorithm to find a common element of the set of fixed points of a nonexpansive mapping and the set of zeros of an inverse strongly-monotone mapping. We obtain a weak convergence theorem in Hilbert space. In particular, the set of zero points of an inverse strongly-monotone mapping can be transformed into the solution set of the variational inequality problem. Further, based on this result, we also obtain some new weak convergence theorems which are used to solve the equilibrium problem and the split feasibility problem. View Full-Text
Keywords: Yamada iteration; nonexpansive mappings; inverse strongly-monotone mappings; variational inequality; zero point; iterative method; fixed point Yamada iteration; nonexpansive mappings; inverse strongly-monotone mappings; variational inequality; zero point; iterative method; fixed point
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Tian, M.; Tong, M.-Y. Extension and Application of the Yamada Iteration Algorithm in Hilbert Spaces. Mathematics 2019, 7, 215.

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