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

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Advances in Metric Fixed Point Theory and Applications

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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 \({(H_h)}\) 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.

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Acknowledgements

This research was supported by Ministry of Education and Training of Vietnam under grant number B2021.SPD.03.

Author information

Authors and Affiliations

  1. Department of Scientific Fundamentals, Posts and Telecommunications Institute of Technology, Ho Chi Minh City, Vietnam

    Nguyen Van Hung

  2. Department of Mathematics, Vinh University, Nghe An, Vietnam

    Dinh Huy Hoang

  3. Department of Mathematics, Dong Thap University, Cao Lanh City, Dong Thap, Vietnam

    Vo Minh Tam

  4. Department of Mathematics Education, Gyeongsang National University, Jinju, 52828, Korea

    Yeol Je Cho

  5. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, 611731, Sichuan, People’s Republic of China

    Yeol Je Cho

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  1. Nguyen Van Hung
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  2. Dinh Huy Hoang
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Corresponding author

Correspondence to Nguyen Van Hung .

Editor information

Editors and Affiliations

  1. Department of Mathematics Education, Gyeongsang National University, Jinju, Korea (Republic of)

    Yeol Je Cho

  2. Department of Mathematics, King Saud University, Riyadh, Saudi Arabia

    Mohamed Jleli

  3. Department of Mathematics, Aligarh Muslim University, Aligarh, India

    Mohammad Mursaleen

  4. Department of Mathematics, King Saud University, Riyadh, Saudi Arabia

    Bessem Samet

  5. Department of Mathematics and Computer Sciences, University of Palermo, Palermo, Italy

    Calogero Vetro

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Van Hung, N., Hoang, D.H., Tam, V.M., Cho, Y.J. (2021). Convergence Analysis of Solution Sets for Minty Vector Quasivariational Inequality Problems in Banach Spaces. In: Cho, Y.J., Jleli, M., Mursaleen, M., Samet, B., Vetro, C. (eds) Advances in Metric Fixed Point Theory and Applications. Springer, Singapore. https://doi.org/10.1007/978-981-33-6647-3_18

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