Abstract
In his paper Smajdor (Aequat. Math. 75 149–162, 2008) showed that the equation H + tH 2 = (I + tH) ○ H, t ≥ 0 is a necessary and sufficient condition under which the family {F t, t ≥ 0} of set-valued functions \({F^t(x):=\sum_{n=0}^{\infty} \frac{t^n}{n!}H^n(x), x \in K}\) is an iteration semigroup. We present a simple proof of a generalization of this result, independent of the coefficients of the series.
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Szczawińska, J. On some equation for set-valued functions. Aequat. Math. 85, 421–428 (2013). https://doi.org/10.1007/s00010-012-0139-9
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DOI: https://doi.org/10.1007/s00010-012-0139-9