Continuous selections avoiding extreme points

It is shown that if X is a countably paracompact collectionwise normal space, Y is a Banach space and phi : X -> 2(Y) is a lower semicontinuous mapping such that phi(x) is Y or a compact convex subset with Card phi(x) > 1 for each X epsilon X, then phi admits a continuous selection f : X -> Y such that f (x) is not an extreme point of phi(x) for each X E X. This is an affirmative answer to the problem posed by V. Gutev, H. Ohta and K. Yamazaki [V. Gutev, H. Ohta and K. Yamazaki, Selections and sandwich-like properties via semi-continuous Banach-valued functions, J. Math. Soc. Japan 55 (2003) 499-521]. (c) 2007 Elsevier B.V. All rights reserved.