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

Shih-sen Chang (), Liangcai Zhao () and Zhaoli Ma ()
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Shih-sen Chang: China Medical University, Center for General Education
Liangcai Zhao: Yibin University, College of Mathematics
Zhaoli Ma: Yunnan Open University (Yunnan Technical College of National Defence Industry), College of public foundation

Chapter Chapter 3 in Advances in Metric Fixed Point Theory and Applications, 2021, pp 41-59 from Springer

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 the split variational inclusion problem and the 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 the problems for an asymptotically nonexpansive semigroup. As applications, we utilize the results to study the split optimization problem and the split variational inequality.

Keywords: Split variational inclusion problem; Asymptotically nonexpansive semigroup; Fixed point problem; Nonexpansive semigroup; 54E70; 47H25 (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-981-33-6647-3_3

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DOI: 10.1007/978-981-33-6647-3_3

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