On regular multivalued cosine families
Abstract
Let K be a convex cone in a real normed space X. A one-parameter family {Ft : t ≥ 0} of set-valued functions Ft :K→n(K), where n(K) := {D : D ⊂ K, D ≠ ⌀}, is called cosine iff Ft+s + Ft-s = 2Ft◦Fs, whenever 0 ≤ s ≤ t and F0 is the identity map. A cosine family {Ft : t > 0} is regular iff limt→0+Ft(x) = {x} for every x.
The growth and the continuity of regular cosine families are investigated.
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Wyższa Szkoła Pedagogiczna im. Komisji Edukacji Narodowej w Krakowie Poland
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