Article
Keywords:
compact map; compact $R_\delta$-set
Summary:
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 $R_\delta$.
References:
[2] E. F. Beckenbach, R. Bellman:
Inequalities. Springer-Verlag, Berlin-Göttingen-Heidelberg, 1961.
MR 0158038 |
Zbl 0186.09606
[6] K. Czarnowski, T. Pruszko:
On the structure of fixed point sets of compact maps in $B_0$ spaces with applications to integral and differential equations in unbounded domain. J. Math. Anal. Appl. 154 (1991), 151-163.
DOI 10.1016/0022-247X(91)90077-D |
MR 1087965
[7] V. Šeda, Z. Kubáček: On the set of fixed points of a compact operator. Czech. Math. J., to appear.