METRIC REGULARITY OF COMPOSITE MULTIFUNCTIONS IN BANACH SPACES

Abstract

We consider metric regularity of composite multifucntions and establish an inequality on the moduli of metric regularity. Refining the original proofs of the Robinson-Ursescu theorem and Lyusternik-Graves theorem, we give an unified analysis for these two theorems, applicable to the composite of a closed convex multifunction and a continuous function.