Binding Non-convex Multi-valued Mapping Of Calmness

In this paper,we mainly discuss calmness for L-subsmooth multifunction in the constraint setting, using technique and method of variational analysis.We provide some sufficient and necessary conditions of the calmness in Banach spaces,and sharper results obtained in Asplund spaces.We also give the necessary and suffi-cient conditions of strong calmness of such mapping.Finally, we consider formulas and conclusions of modulus of calmness for nonconvex constraint multifunctions.