# Concave iteration semigroups of linear set-valued functions

Annales Polonici Mathematici (1999)

- Volume: 71, Issue: 1, page 31-38
- ISSN: 0066-2216

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topJolanta Olko. "Concave iteration semigroups of linear set-valued functions." Annales Polonici Mathematici 71.1 (1999): 31-38. <http://eudml.org/doc/262562>.

@article{JolantaOlko1999,

abstract = {We consider a concave iteration semigroup of linear continuous set-valued functions defined on a closed convex cone in a separable Banach space. We prove that such an iteration semigroup has a selection which is also an iteration semigroup of linear continuous functions. Moreover it is majorized by an "exponential" family of linear continuous set-valued functions.},

author = {Jolanta Olko},

journal = {Annales Polonici Mathematici},

keywords = {linear set-valued function; concave set-valued function; iteration semigroup; linear multivalued map; concave iteration semigroup; infinitesimal generator; selection},

language = {eng},

number = {1},

pages = {31-38},

title = {Concave iteration semigroups of linear set-valued functions},

url = {http://eudml.org/doc/262562},

volume = {71},

year = {1999},

}

TY - JOUR

AU - Jolanta Olko

TI - Concave iteration semigroups of linear set-valued functions

JO - Annales Polonici Mathematici

PY - 1999

VL - 71

IS - 1

SP - 31

EP - 38

AB - We consider a concave iteration semigroup of linear continuous set-valued functions defined on a closed convex cone in a separable Banach space. We prove that such an iteration semigroup has a selection which is also an iteration semigroup of linear continuous functions. Moreover it is majorized by an "exponential" family of linear continuous set-valued functions.

LA - eng

KW - linear set-valued function; concave set-valued function; iteration semigroup; linear multivalued map; concave iteration semigroup; infinitesimal generator; selection

UR - http://eudml.org/doc/262562

ER -

## References

top- [1] C. Castaing and M. Valadier, Convex Analysis and Measurable Multifunctions, Lecture Notes in Math. 580, Springer, Berlin, 1977. Zbl0346.46038
- [2] M. Kisielewicz, Differential Inclusions and Optimal Control, PWN, Warszawa, and Kluwer, Dordrecht, 1991.
- [3] K. Nikodem, K-convex and K-concave set-valued functions, Zeszyty Nauk. Politech. Łódz. Mat. 559, Rozprawy Nauk. 114, Łódź, 1989.
- [4] J. Olko, Semigroups of set-valued functions, Publ. Math. Debrecen 51 (1997), 81-96.
- [5] J. Plewnia, On a family of set valued functions, Publ. Math. Debrecen 46 (1995), 149-159. Zbl0862.54015
- [6] A. Smajdor, Additive selections of a composition of additive set-valued functions, in: Iteration Theory (Batschuns, 1992), World Sci., 1996, 251-254. Zbl0914.39032
- [7] A. Smajdor, Increasing iteration semigroups of Jensen set-valued functions, Aequationes Math. 56 (1998), 131-142. Zbl0913.39013

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