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 → 2 Y is a lower semicontinuous mapping such that φ ( x ) is Y or a compact convex subset with Card φ ( 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].