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

Mathematica Bohemica (1993)

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

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topKubáček, 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

top- N. Aronszajn, 10.2307/1968963, Ann. Math. 43 (1942), 730-738. (1942) Zbl0061.17106MR0007195DOI10.2307/1968963
- E. F. Beckenbach, R. Bellman, Inequalities, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1961. (1961) Zbl0186.09606MR0158038
- I. Bihari, 10.1007/BF02022967, Acta Math. Acad. Sci. Hung. 7 (1956), 81-94. (1956) Zbl0070.08201MR0079154DOI10.1007/BF02022967
- K. Borsuk, Theory of retracts, PWN, Warszawa, 1967. (1967) Zbl0153.52905MR0216473
- 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
- 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
- V. Šeda, Z. Kubáček, On the set of fixed points of a compact operator, Czech. Math. J., to appear.
- 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
- 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

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

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