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Iteration regularized semigroups of set-valued functions

Mosallanezhad M., Janfada M.

Journal of Applied Analysis

2016

Vol. 22, nr 2

121--130

In this paper, a set-valued iteration regularized semigroup, i.e. a family {Ft}t≥0 of set-valued functions for which Fs+t∘C=Fs∘Ft,F0=C,s,t≥0, will be considered, where C is a set-valued function on a closed convex cone in a Banach space. Under some appropriate conditions the generator of a set-valued regularized concave semigroup is introduced and some of its properties are investigated. Also differentiability of the iteration family {C∘ Ft}t≥0 is discussed.

Cocycles of continuous iteration semigroups

Guzik G., Jarczyk W., Matkowski J.

Bulletin of the Polish Academy of Sciences. Mathematics

2003

Vol. 51, no 2

185-197

We give the form of all continuous cocycles of continuous iteration semigroups, mapping the product of the positive half-line and an interval into a topological group.