Concave iteration semigroups of linear set-valued functions

Jolanta Olko

Annales Polonici Mathematici (1999)

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

Abstract

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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.

How to cite

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Jolanta 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

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

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