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A characterization of generalized Levitin–Polyak well-posedness for parametric symmetric strong vector quasi-equilibrium problems and its application

A characterization of generalized Levitin–Polyak well-posedness for parametric symmetric strong vector quasi-equilibrium problems and its application

Nguyễn Văn Hưng

This paper aims to investigate the Levitin–Polyak (LP)-wellposedness of parametric symmetric strong vector quasi-equilibrium problems. Firstly, we consider symmetric strong vector quasiequilibrium problems under perturbations. Secondly, we study the concept of upper semicontinuity in the setting of variable conic structures for vector-valued mappings and explore their properties. Thirdly, we establish the LP-well-posedness and generalized LP-well-posedness for these problems under appropriate conditions. Furthermore, employing the Hausdorff measure to assess non-compactness, we investigate the metric characterization of generalized LP-well-posedness for parametric symmetric strong vector quasi-equilibrium problems. As a final application, we delve into the LP-well-posedness of symmetric strong vector quasi-variational inequality problems. The results in this paper are novel and enhance several key findings in the existing literature. To illustrate these results, we present multiple examples.

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A characterization of generalized Levitin–Polyak well-posedness for parametric symmetric strong vector quasi-equilibrium problems and its application


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Từ khoá:

Symmetric strong vector quasi-equilibrium problems; Levitin–Polyak well-posedness; Levitin–Polyak well-posedness in the generalized sense; symmetric strong vector quasi-variational inequality problems