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

In: Advances in Metric Fixed Point Theory and Applications

Author

Listed:
  • 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)

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.

Suggested Citation

  • Shih-sen Chang & Liangcai Zhao & Zhaoli Ma, 2021. "Split Variational Inclusion Problem and Fixed Point Problem for Asymptotically Nonexpansive Semigroup with Application to Optimization Problem," Springer Books, in: Yeol Je Cho & Mohamed Jleli & Mohammad Mursaleen & Bessem Samet & Calogero Vetro (ed.), Advances in Metric Fixed Point Theory and Applications, chapter 0, pages 41-59, Springer.
    • Handle: RePEc:spr:sprchp:978-981-33-6647-3_3
    DOI: 10.1007/978-981-33-6647-3_3
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