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Well-posedness for generalized mixed vector variational-like inequality problems in Banach space. (English) Zbl 1384.49024

Summary: In this article, we focus to study well-posedness of a generalized mixed vector variational-like inequality and optimization problems with aforesaid inequality as constraint. We establish a metric characterization of well-posedness in terms of approximate solution set. Thereafter, we prove sufficient conditions of generalized well-posedness by assuming the boundedness of approximate solution set. We also prove that the well-posedness of considered optimization problems is closely related to that of generalized mixed vector variational-like inequality problems. Moreover, we present some examples to investigate the results established in this paper.

MSC:

49K40 Sensitivity, stability, well-posedness
54C60 Set-valued maps in general topology
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
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