与渐进非扩张半群不动点问题有关的分裂变分包含问题及其对最优化问题的应用

Acta mathematica scientia,Series A ›› 2018, Vol. 38 ›› Issue (2): 231-243.

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Split Variational Inclusion Problem Involving Fixed Point for an Asymptotically Nonexpansive Semigroup with Application to Optimization Problem

Chang Shih-sen¹, Liu Zhenhai², Wen Ching-Feng³, Tang Jinfang⁴

1. Center for General Education, China Medical University, Taiwan Taichung 40402;
2. Guangxi University for Nationalities, Nanning, Guangxi 53006;
3. Center for Fundamental Science, Kaohsiung Medical University, Taiwan Kaohsiung 80708;
4. Yibin University, Sichuan Yibin 644007

Received:2016-07-21 Revised:2017-04-29 Online:2018-04-26 Published:2018-04-26
Supported by:
Supported by the NSFC (11671101), the Guangxi Special Fund for Qutstanding Experts, the Natural Science Foundation of Taichung China Medical University and Nonlinear Analysis and Optimization Research Center of Kaohsiung Medical University, and the Scientific Research Fund of Sichuan Provincial Department of Science and Technology (2015JY0165)

Abstract

Abstract: The purpose of this paper is by using the shrinking projection method to introduce and study an iterative process to approximate a common solution of split variational inclusion problem and fixed point problem for an asymptotically nonexpansive semigroup in real Hilbert spaces. Further, we prove that the sequences generated by the proposed iterative method converge strongly to a common solution of split variational inclusion problem and fixed point problem for an asymptotically nonexpansive semigroup. As applications, we shall utilize the results to study the split optimization problem and the split variational inequality.

Key words: Split variational inclusion problem, Asymptotically nonexpansive semigroup, Fixed point problem, Nonexpansive semigroup

CLC Number:

O177.91

Chang Shih-sen, Liu Zhenhai, Wen Ching-Feng, Tang Jinfang. Split Variational Inclusion Problem Involving Fixed Point for an Asymptotically Nonexpansive Semigroup with Application to Optimization Problem[J].Acta mathematica scientia,Series A, 2018, 38(2): 231-243.

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Split Variational Inclusion Problem Involving Fixed Point for an Asymptotically Nonexpansive Semigroup with Application to Optimization Problem

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