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<p>In this paper, we formulate the classical well-posedness and generalized well-posedness concepts for a class of split mixed vector quasivariational inequality problems (SMVqVIP). We provide metric characterization results for the well-posedness properties of the considered problem based on its relation with its approximating solution set. In our study, we use the well-known concepts of Hausdorff metric and Kuratowski’s measure of noncompactness. We also present several examples to illustrate the proven results. Finally, we establish the equivalence of the well-posedness of our considered problem with the existence and uniqueness of its solution.</p>

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Well-posedness of split mixed vector quasivariational inequality problem

  • 期刊论文

  • 发表日期：

    2025年8月6日

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  • Sumit Gupta,
  • Prashanta Majee

摘要

In this paper, we formulate the classical well-posedness and generalized well-posedness concepts for a class of split mixed vector quasivariational inequality problems (SMVqVIP). We provide metric characterization results for the well-posedness properties of the considered problem based on its relation with its approximating solution set. In our study, we use the well-known concepts of Hausdorff metric and Kuratowski’s measure of noncompactness. We also present several examples to illustrate the proven results. Finally, we establish the equivalence of the well-posedness of our considered problem with the existence and uniqueness of its solution.