On measures of noncompactness in topological vector spaces

Bogdan Rzepecki

Commentationes Mathematicae Universitatis Carolinae (1982)

  • Volume: 023, Issue: 1, page 105-116
  • ISSN: 0010-2628

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Rzepecki, Bogdan. "On measures of noncompactness in topological vector spaces." Commentationes Mathematicae Universitatis Carolinae 023.1 (1982): 105-116. <http://eudml.org/doc/17164>.

@article{Rzepecki1982,
author = {Rzepecki, Bogdan},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {system of ordinary differential equations in Banach spaces; Kuratowski measure of noncompactness; fixed point theorems of Darbo type; axiomatic concept for measure of noncompactness; measure of weak noncompactness; weak solutions; compact and connected set in the space of weakly continuous functions; topology of weak-uniform convergence},
language = {eng},
number = {1},
pages = {105-116},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On measures of noncompactness in topological vector spaces},
url = {http://eudml.org/doc/17164},
volume = {023},
year = {1982},
}

TY - JOUR
AU - Rzepecki, Bogdan
TI - On measures of noncompactness in topological vector spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1982
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 023
IS - 1
SP - 105
EP - 116
LA - eng
KW - system of ordinary differential equations in Banach spaces; Kuratowski measure of noncompactness; fixed point theorems of Darbo type; axiomatic concept for measure of noncompactness; measure of weak noncompactness; weak solutions; compact and connected set in the space of weakly continuous functions; topology of weak-uniform convergence
UR - http://eudml.org/doc/17164
ER -

References

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  1. A. AMBROSETTI, Un teorema di esistenza per le equazioni differenziali negli spazi di Banach, Rend. Sem. Mat. Padova 39 (1967), 349-360. (1967) Zbl0174.46001MR0222426
  2. C. BERGE, Topological Spaces, Edinburgh and London, 1963. (1963) Zbl0114.38602
  3. E. CRAMER V. LAKSHMIKANTHAN A. R. MITCHELL, On the existence of weak solutions of differential equations in nonreflexive Banach spaces, Nonlinear Analysis. Theory, Methods and Applications 2 (1978), 169-177. (1978) MR0512280
  4. J. DANEŠ, Some fixed point theorems, Comment. Math. Univ. Carolinae 9 (1968), 223-235. (1968) MR0235435
  5. G. DARBO, Punti uniti in transformazioni a codomino non compatto, Rend. Sem. Mat. Univ. Padova 24 (1955), 84-92. (1955) MR0070164
  6. F. DE BLASI, On a property of the unit sphere in a Banach space, Bull. Math, de la Soc. Sci. de la R.S. de Roumanie 21 (69) (1977), 259-262. (1977) Zbl0365.46015MR0482402
  7. K. DEIMLING, Ordinary Differential Equations in Banach Spaces, Lect. Notes in Math. 596, Springer-Verlag, 1977. (1977) Zbl0361.34050MR0463601
  8. K. KURATOWSKI, Topologie. Vol. 1, Academic Press, New York, 1966. (1966) MR0217751
  9. R. H. MARTIN, Jr., Nonlinear Operators and Differential Equations in Banach Spaces, John Wiley and Sons, New York, 1976. (1976) Zbl0333.47023MR0492671
  10. M. Z. NASHED J. S. W. WONG, Some variants of a fixed point theorem of Krasnoselskii and applications to non-linear integral equations, J. Math. Mech. 18 (1969), 767-777. (1969) MR0238140
  11. J. M. ORTEGA W. C. RHEINBOLDT, Iterative Solutions of Nonlinear Equations in Several Variables, Academic Press, New York, 1970. (1970) MR0273810
  12. B. RZEPECKI, Differential equations in linear spaces, Ph.D. Thesis. A. Mickiewicz University, Poznań 1976. (1976) 
  13. B. RZEPECKI, On the method of Euler polygons for the differential equations in locally convex spaces, Bull. Acad. Polon. Sci., Sér. Sci. Math. Astronom. Phys. 23 (1975), 411-414. (1975) MR0374593
  14. B. RZEPECKI, A functional differential equation in m Banach space, Ann. Polon. Math. 36 (1979), 95-100. (1979) MR0529310
  15. B. N. SADOVSKII, Limit compact and condensing operators, Russian Math. Surveys 27 (1972), 86-144. (1972) MR0428132
  16. A. SZÉP, Existence theorem for weak solutions of ordinary differential equations in reflexive Banach spaces, Studia Scientiarum Math. Hungarica 6 (1971), 197-203. (1971) MR0330688
  17. S. SZUFLA, Some remarks on ordinary differential equations in Banach space, Bull. Acad. Polon. Sci., Sér. Sci. Math. Astronom. Phys. 16 (1968), 795-800. (1968) MR0239238
  18. S. SZUFLA, Kneser's theorem for weak solutions of ordinary differential equations in reflexive Banach spaces, Bull. Acad. Polon. Sci., Sér. Sci. Math. Astronom. Phys. 26 (1978), 407-413. (1978) Zbl0384.34039MR0492684

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