Abstract
Let X be an arbitrary set. We characterize all interval-valued functions \({A:X\to 2^\mathbb{R}}\) for which a multifunction \({F:(0,\infty)\times X\to 2^X}\) of the form \({F(t,x)=A^{-}\big(A(x)+\min \{t,q-\inf A(x)\}\big)}\), where \({q=\sup A(X)}\), is an iteration semigroup. The multifunction F is the set-valued counterpart of the fundamental form of continuous iteration semigroups of single-valued functions on an interval.
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Łydzińska, G. On some set-valued iteration semigroups generated by interval-valued functions. Aequat. Math. 90, 381–391 (2016). https://doi.org/10.1007/s00010-015-0346-2
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DOI: https://doi.org/10.1007/s00010-015-0346-2