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The stability of set of generalized Ky Fan’s points. (English) Zbl 1297.90178

Summary: This paper is concerned with a generalized Ky Fan’s inequality. We first give an existence result of generalized Ky Fan’s (weak) efficient points, and then establish a complete metric space. Based on these results, we obtain the sufficient and necessary conditions of upper semicontinuity of efficient solution mapping to a generalized Ky Fan’s inequality. We also obtain the sufficient conditions of lower semicontinuity and continuity of efficient solution mapping to a generalized Ky Fan’s inequality. Our results are new and different from the corresponding ones in the literature.

MSC:

90C48 Programming in abstract spaces
45M10 Stability theory for integral equations
58C07 Continuity properties of mappings on manifolds
74G15 Numerical approximation of solutions of equilibrium problems in solid mechanics
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