Continuous selections avoiding extreme points

It is shown that if X is a countably paracompact collectionwise normal space, Y is a Banach space and φ:X→Y2 is a lower semicontinuous mapping such that φ(x) is Y or a compact convex subset with Cardφ(x)>1 for each x∈X, then φ admits a continuous selection f:X→Y such that f(x) is not an extreme point of φ(x) for each x∈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].