STABILITY OF GENERALIZED EQUATIONS GOVERNED BY COMPOSITE MULTIFUNCTIONS

摘要

This paper deals with metric regularity of a parametrized epigraphical set-valued mapping associated with a parametrized composition set-valued mapping and also with semiregularity of composition of set-valued mappings. Then, we obtain Lipschitz-likeness, calmness of the implicit set-valued mappings which were defined by the associated generalized equation. Moreover, Robinson's metric regularity of implicit set-valued mappings associated to a composite mapping was also derived when the so-called "local composition stability" is imposed. Our work is new and generalizes the recent results on this topic by Durea, Strugariu [19], Ngai, Tron, Thera [33], Zheng, Ng [45], Durea, Strugariu [18,20], Durea, Huynh, Nguyen, Strugariu [23], and Cibulka, Fabian, Kruger [9].