On the structure of fixed point sets of some compact maps in the Fréchet space

Zbyněk Kubáček

Mathematica Bohemica (1993)

  • Volume: 118, Issue: 4, page 343-358
  • ISSN: 0862-7959

Abstract

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The aim of this note is 1. to show that some results (concerning the structure of the solution set of equations (18) and (21)) obtained by Czarnowski and Pruszko in [6] can be proved in a rather different way making use of a simle generalization of a theorem proved by Vidossich in [8]; and 2. to use a slight modification of the “main theorem” of Aronszajn from [1] applying methods analogous to the above mentioned idea of Vidossich to prove the fact that the solution set of the equation (24), (25) (studied in the paper [7]) is a compact R δ .

How to cite

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Kubáček, Zbyněk. "On the structure of fixed point sets of some compact maps in the Fréchet space." Mathematica Bohemica 118.4 (1993): 343-358. <http://eudml.org/doc/29314>.

@article{Kubáček1993,
abstract = {The aim of this note is 1. to show that some results (concerning the structure of the solution set of equations (18) and (21)) obtained by Czarnowski and Pruszko in [6] can be proved in a rather different way making use of a simle generalization of a theorem proved by Vidossich in [8]; and 2. to use a slight modification of the “main theorem” of Aronszajn from [1] applying methods analogous to the above mentioned idea of Vidossich to prove the fact that the solution set of the equation (24), (25) (studied in the paper [7]) is a compact $R_\delta $.},
author = {Kubáček, Zbyněk},
journal = {Mathematica Bohemica},
keywords = {compact map; compact $R_\delta $-set},
language = {eng},
number = {4},
pages = {343-358},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the structure of fixed point sets of some compact maps in the Fréchet space},
url = {http://eudml.org/doc/29314},
volume = {118},
year = {1993},
}

TY - JOUR
AU - Kubáček, Zbyněk
TI - On the structure of fixed point sets of some compact maps in the Fréchet space
JO - Mathematica Bohemica
PY - 1993
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 118
IS - 4
SP - 343
EP - 358
AB - The aim of this note is 1. to show that some results (concerning the structure of the solution set of equations (18) and (21)) obtained by Czarnowski and Pruszko in [6] can be proved in a rather different way making use of a simle generalization of a theorem proved by Vidossich in [8]; and 2. to use a slight modification of the “main theorem” of Aronszajn from [1] applying methods analogous to the above mentioned idea of Vidossich to prove the fact that the solution set of the equation (24), (25) (studied in the paper [7]) is a compact $R_\delta $.
LA - eng
KW - compact map; compact $R_\delta $-set
UR - http://eudml.org/doc/29314
ER -

References

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  1. N. Aronszajn, 10.2307/1968963, Ann. Math. 43 (1942), 730-738. (1942) Zbl0061.17106MR0007195DOI10.2307/1968963
  2. E. F. Beckenbach, R. Bellman, Inequalities, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1961. (1961) Zbl0186.09606MR0158038
  3. I. Bihari, 10.1007/BF02022967, Acta Math. Acad. Sci. Hung. 7 (1956), 81-94. (1956) Zbl0070.08201MR0079154DOI10.1007/BF02022967
  4. K. Borsuk, Theory of retracts, PWN, Warszawa, 1967. (1967) Zbl0153.52905MR0216473
  5. F. F. Browder, G. P. Gupta, 10.1016/0022-247X(69)90162-0, J. Math. Anal. Appl. 26 (1969), 390-402. (1969) MR0257826DOI10.1016/0022-247X(69)90162-0
  6. K. Czarnowski, T. Pruszko, 10.1016/0022-247X(91)90077-D, J. Math. Anal. Appl. 154 (1991), 151-163. (1991) MR1087965DOI10.1016/0022-247X(91)90077-D
  7. V. Šeda, Z. Kubáček, On the set of fixed points of a compact operator, Czech. Math. J., to appear. 
  8. G. Vidossich, 10.1016/0022-247X(71)90040-0, J. Math. Anal. Appl. 36 (1971), 581-587. (1971) Zbl0194.44903MR0285945DOI10.1016/0022-247X(71)90040-0
  9. G. Vidossich, 10.1016/0022-247X(71)90100-4, J. Math. Anal. Appl. 34 (1971), 602-617. (1971) MR0283645DOI10.1016/0022-247X(71)90100-4

Citations in EuDML Documents

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  1. Daria Bugajewska, On the structure of solution sets of differential equations in Banach spaces
  2. Zbyněk Kubáček, On the structure of the solution set of a functional-differential system on an unbounded interval
  3. Mária Kečkemétyová, On the structure of the set of solutions of nonlinear boundary value problems for ODEs on unbounded intervals
  4. Valter Šeda, On condensing discrete dynamical systems
  5. Lech Górniewicz, Topological structure of solution sets: current results

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