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Painlevé–Kuratowski Convergence of Solutions for Perturbed Symmetric Set-Valued Quasi-Equilibrium Problem via Improvement Sets

Author

Listed:
  • Zai-Yun Peng

    (College of Mathematics and Statistics, Chongqing JiaoTong University, Chongqing 400074, P. R. China)

  • Jing-Jing Wang

    (College of Mathematics and Statistics, Chongqing JiaoTong University, Chongqing 400074, P. R. China)

  • Xian-Jun Long

    (College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, P. R. China)

  • Fu-Ping Liu

    (School of Mathematical Sciences, Chongqing Normal University, Chongqing 400047, P. R. China)

Abstract

This paper is devoted to study the Painlevé–Kuratowski convergence of solution sets for perturbed symmetric set-valued quasi-equilibrium problems (SSQEP)n via improvement sets. By virtue of the oriented distance function, the sufficient conditions of Painlevé–Kuratowski convergence of efficient solution sets for (SSQEP)n are obtained through a new nonlinear scalarization technical. Then, under ΓC-convergence of set-valued mappings, the Painlevé–Kuratowski convergence of weak efficient solution sets for (SSQEP)n is discussed. What’s more, with suitable convergence assumptions, we also establish the sufficient conditions of lower Painlevé–Kuratowski convergence of Borwein proper efficient solution sets for (SSQEP)n under improvement sets. Some interesting examples are formulated to illustrate the significance of the main results.

Suggested Citation

  • Zai-Yun Peng & Jing-Jing Wang & Xian-Jun Long & Fu-Ping Liu, 2020. "Painlevé–Kuratowski Convergence of Solutions for Perturbed Symmetric Set-Valued Quasi-Equilibrium Problem via Improvement Sets," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 37(04), pages 1-22, August.
    • Handle: RePEc:wsi:apjorx:v:37:y:2020:i:04:n:s0217595920400035
    DOI: 10.1142/S0217595920400035
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