Abstract
We give the characterization of set-valued iteration semigroups which are the counterparts of the fundamental form of continuous iteration semigroups of single-valued functions on an interval.
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Guzik G., Jarczyk W., Matkowski J.: Cocycles of continuous iteration semigroups. Bull. Polish Acad. Sci. Math. 51, 187–197 (2003)
Kuczma, M.: Functional equations in a single variable. Monografie Matematyczne. vol. 46, PWN-Polish Scientific Publishers, Warszawa (1968)
Kuczma, M., Choczewski, B., Ger, R.: Iterative functional equations, Encyclopedia of Mathematics and its Applications. vol. 32, Cambridge University Press, Cambridge (1990)
Łydzińska G.: Iteration families for which expansion implies collapse. Aeqationes Math. 70, 247–253 (2005)
Łydzińska G.: On collapsing iteration semigroups of set-valued functions. Publ. Math. Debrecen 64, 285–298 (2004)
Łydzińska G.: On expanding iteration semigroups of set-valued functions. Math.Pannon. 15, 55–64 (2004)
Łydzińska G.: On lower semicontinuity of some set-valued iteration semigroups. Nonlinear Anal. 71, 5644–5654 (2009)
Targonski, Gy.: Topics in Iteration Theory. Vandenhoeck and Ruprecht, Göttingen (1981)
Smajdor, A.: Iterations of Multi-valued Functions. Prace Naukowe Uniwersytetu Śla̧skiego w Katowicach, vol. 759 (1985)
Smajdor A.: On concave iteration semigroups of linear set-valued functions. Aequationes Math. 75, 149–162 (2008)
Olko J.: Selections of an iteration semigroup of linear set-valued functions. Aequationes Math. 56, 157–168 (1998)
Zdun M.C.: Continuous and Differentiable Iteration Semigroups. Prace Naukowe Uniwersytetu Śla̧skiego w Katowicach, vol. 308 (1979)
Zdun M.C.: On set-valued iteration groups generated by commuting functions. J. Math. Anal. Appl. 398, 638–648 (2013)
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Łydzińska, G. The characterization of some set-valued iteration semigroups. Aequat. Math. 89, 791–802 (2015). https://doi.org/10.1007/s00010-014-0270-x
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DOI: https://doi.org/10.1007/s00010-014-0270-x