A Komlós-type theorem for the set-valued Henstock-Kurzweil-Pettis integral and applications

Bianca Satco

Czechoslovak Mathematical Journal (2006)

  • Volume: 56, Issue: 3, page 1029-1047
  • ISSN: 0011-4642

Abstract

top
This paper presents a Komlós theorem that extends to the case of the set-valued Henstock-Kurzweil-Pettis integral a result obtained by Balder and Hess (in the integrably bounded case) and also a result of Hess and Ziat (in the Pettis integrability setting). As applications, a solution to a best approximation problem is given, weak compactness results are deduced and, finally, an existence theorem for an integral inclusion involving the Henstock-Kurzweil-Pettis set-valued integral is obtained.

How to cite

top

Satco, Bianca. "A Komlós-type theorem for the set-valued Henstock-Kurzweil-Pettis integral and applications." Czechoslovak Mathematical Journal 56.3 (2006): 1029-1047. <http://eudml.org/doc/31089>.

@article{Satco2006,
abstract = {This paper presents a Komlós theorem that extends to the case of the set-valued Henstock-Kurzweil-Pettis integral a result obtained by Balder and Hess (in the integrably bounded case) and also a result of Hess and Ziat (in the Pettis integrability setting). As applications, a solution to a best approximation problem is given, weak compactness results are deduced and, finally, an existence theorem for an integral inclusion involving the Henstock-Kurzweil-Pettis set-valued integral is obtained.},
author = {Satco, Bianca},
journal = {Czechoslovak Mathematical Journal},
keywords = {Komlós convergence; Henstock-Kurzweil integral; Henstock-Kurzweil-Pettis set-valued integral; selection; Komlós convergence},
language = {eng},
number = {3},
pages = {1029-1047},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A Komlós-type theorem for the set-valued Henstock-Kurzweil-Pettis integral and applications},
url = {http://eudml.org/doc/31089},
volume = {56},
year = {2006},
}

TY - JOUR
AU - Satco, Bianca
TI - A Komlós-type theorem for the set-valued Henstock-Kurzweil-Pettis integral and applications
JO - Czechoslovak Mathematical Journal
PY - 2006
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 56
IS - 3
SP - 1029
EP - 1047
AB - This paper presents a Komlós theorem that extends to the case of the set-valued Henstock-Kurzweil-Pettis integral a result obtained by Balder and Hess (in the integrably bounded case) and also a result of Hess and Ziat (in the Pettis integrability setting). As applications, a solution to a best approximation problem is given, weak compactness results are deduced and, finally, an existence theorem for an integral inclusion involving the Henstock-Kurzweil-Pettis set-valued integral is obtained.
LA - eng
KW - Komlós convergence; Henstock-Kurzweil integral; Henstock-Kurzweil-Pettis set-valued integral; selection; Komlós convergence
UR - http://eudml.org/doc/31089
ER -

References

top
  1. 10.1016/0022-247X(90)90237-A, J.  Math. Anal. Appl. 151 (1990), 1–16. (1990) Zbl0733.46015MR1069442DOI10.1016/0022-247X(90)90237-A
  2. Two generalizations of Komlós theorem with lower closure-type applications, J.  Convex Anal. 3 (1996), 25–44. (1996) MR1422749
  3. 10.4064/ba52-1-6, Bull. Pol. Acad. Sci. Math. 52 (2004), 53–61. (2004) MR2070028DOI10.4064/ba52-1-6
  4. Weak compactness and convergences in Bochner and Pettis integration, Vietnam J.  Math. 24 (1996), 241–286. (1996) MR2010821
  5. 10.1007/BF01776856, Ann. Mat. Pura Appl. 140 (1985), 345–364. (1985) MR0807644DOI10.1007/BF01776856
  6. 10.1007/BFb0087688, Lect. Notes Math. Vol.  580, Springer-Verlag, Berlin, 1977. (1977) MR0467310DOI10.1007/BFb0087688
  7. On x ' = f ( t , x ) and Henstock-Kurzweil integrals, Differential Integral Equations 4 (1991), 861–868. (1991) MR1108065
  8. 10.1023/B:CMAJ.0000042368.51882.ab, Czechoslovak Math.  J. 54 (2004), 279–289. (2004) MR2059250DOI10.1023/B:CMAJ.0000042368.51882.ab
  9. 10.1023/A:1026547222209, Set-Valued Analysis 8 (2000), 329–360. (2000) MR1802239DOI10.1023/A:1026547222209
  10. Linear integral equations of Volterra concerning Henstock integrals, Real Anal. Exchange 25 (1999/00), 389–417. (1999/00) MR1758896
  11. Impulsive retarded differential equations in Banach spaces via Bochner-Lebesgue and Henstock integrals, Nonlinear Anal. Ser.  A: Theory Methods 50 (2002), 389–407. (2002) MR1906469
  12. On Denjoy-Dunford and Denjoy-Pettis integrals, Studia Math. 130 (1998), 115–133. (1998) MR1623348
  13. 10.4064/sm-92-1-73-91, Studia Math. 92 (1989), 73–91. (1989) Zbl0681.28006MR0984851DOI10.4064/sm-92-1-73-91
  14. 10.1090/gsm/004/09, Grad. Stud. Math. Vol  4, AMS, Providence, 1994. (1994) Zbl0807.26004MR1288751DOI10.1090/gsm/004/09
  15. 10.1016/0047-259X(91)90012-Q, J.  Multivariate Anal. 39 (1991), 175–201. (1991) Zbl0746.60051MR1128679DOI10.1016/0047-259X(91)90012-Q
  16. Théorème de Komlós pour des multifonctions intégrables au sens de Pettis et applications, Ann. Sci. Math. Québec 26 (2002), 181–198. (2002) MR1980843
  17. 10.1007/BF02020976, Acta Math. Acad. Sci. Hungar. 18 (1967), 217–229. (1967) MR0210177DOI10.1007/BF02020976
  18. Topics in the theory of Pettis integration. In: School of Measure theory and Real Analysis, Grado, Italy, May  1992, Rend. Ist. Mat. Univ. Trieste 23 (1991), 177–262. (1991) MR1248654
  19. 10.1007/s11228-004-0934-0, Set-Valued Analysis 13 (2005), 167–179. (2005) MR2148134DOI10.1007/s11228-004-0934-0
  20. The Perron integral in ordinary differential equations, Differential Integral Equations 6 (1993), 863–882. (1993) Zbl0784.34006MR1222306

NotesEmbed ?

top

You must be logged in to post comments.