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Convergence Analysis of Solution Sets for Minty Vector Quasivariational Inequality Problems in Banach Spaces

In: Advances in Metric Fixed Point Theory and Applications

Author

Listed:
  • Nguyen Van Hung

    (Posts and Telecommunications Institute of Technology, Department of Scientific Fundamentals)

  • Dinh Huy Hoang

    (Vinh University, Department of Mathematics)

  • Vo Minh Tam

    (Dong Thap University, Department of Mathematics)

  • Yeol Je Cho

    (Gyeongsang National University, Department of Mathematics Education
    University of Electronic Science and Technology of China, School of Mathematical Sciences)

Abstract

In this paper, we consider convergence analysis of the solution sets for vector quasi-variational inequality problems of the Minty type. Based on the nonlinear scalarization function, we obtain a key assumption $${(H_h)}$$ ( H h ) by virtue of a sequence of gap functions. Then we establish the necessary and sufficient conditions for the Painlevé–Kuratowski lower convergence and Painlevé–Kuratowski convergence.

Suggested Citation

  • Nguyen Van Hung & Dinh Huy Hoang & Vo Minh Tam & Yeol Je Cho, 2021. "Convergence Analysis of Solution Sets for Minty Vector Quasivariational Inequality Problems in Banach Spaces," 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 441-460, Springer.
    • Handle: RePEc:spr:sprchp:978-981-33-6647-3_18
    DOI: 10.1007/978-981-33-6647-3_18
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