Metric Subregularity For The Multifunction In L~2Spaces

In this paper, we study the metric regularity in terms of the Proximal Coderiva-tive D*F(x, y)(y*) constructed by the corresponding Proximal Normal cone NP(A, a) in C2. And then, we give a sufficient condition for a multifunction F to be metrically subregular at (a, b) by a variational principle. Our results improve corresponding results in the literature since D*p(x,y)(y*) has a kind of variational behavior of "order two".