On the statistical convergence of nested sequences of sets
Problemy analiza, Tome 11 (2022) no. 3, pp. 3-14.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we show that Wijsman convergence and statistical Wijsman convergence are equivalent to each other if we choose the sequences of sets as monotone. Then, we show that every statistical Wijsman convergent monotone sequence of sets is not only Hausdorff convergent but also statistical Hausdorff convergent to the same set.
Keywords: nested sequences of sets, statistical Wijsman convergence, statistical Hausdorff convergence.
@article{PA_2022_11_3_a0,
     author = {H. Albayrak and F. Babaarslan and \"O. \"Olmez and S. Aytar},
     title = {On the statistical convergence of nested sequences of sets},
     journal = {Problemy analiza},
     pages = {3--14},
     publisher = {mathdoc},
     volume = {11},
     number = {3},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PA_2022_11_3_a0/}
}
TY  - JOUR
AU  - H. Albayrak
AU  - F. Babaarslan
AU  - Ö. Ölmez
AU  - S. Aytar
TI  - On the statistical convergence of nested sequences of sets
JO  - Problemy analiza
PY  - 2022
SP  - 3
EP  - 14
VL  - 11
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PA_2022_11_3_a0/
LA  - en
ID  - PA_2022_11_3_a0
ER  - 
%0 Journal Article
%A H. Albayrak
%A F. Babaarslan
%A Ö. Ölmez
%A S. Aytar
%T On the statistical convergence of nested sequences of sets
%J Problemy analiza
%D 2022
%P 3-14
%V 11
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PA_2022_11_3_a0/
%G en
%F PA_2022_11_3_a0
H. Albayrak; F. Babaarslan; Ö. Ölmez; S. Aytar. On the statistical convergence of nested sequences of sets. Problemy analiza, Tome 11 (2022) no. 3, pp. 3-14. http://geodesic.mathdoc.fr/item/PA_2022_11_3_a0/

[1] Apreutesei G., “Set convergence and the class of compact subsets”, An. Ştiinţ. Univ. Al. I. Cuza Iaşi. Mat., 47:2 (2001), 263–276 | MR | Zbl

[2] Beer G., “On convergence of closed sets in a metric space and distance functions”, Bull. Aust. Math. Soc., 31:3 (1985), 421–432 | DOI | MR | Zbl

[3] Castaing C., Valadier M., Convex analysis and measurable multifunctions, Lecture Notes in Mathematics, Springer-Verlag, Berlin-New York, 1977 | DOI | MR | Zbl

[4] Fast H., “Sur la convergence statistique”, Colloq. Math., 2 (1951), 241–244 | DOI | MR | Zbl

[5] Freedman A. R., Sember J. J., “Densities and summability”, Pacific J. Math., 95:2 (1981), 293–305 | DOI | MR | Zbl

[6] Hausdorff F., Grundzuge der Mengenlehre, Verlag von Veit Comp., Leipzig, 1914 | MR

[7] Kuratowski K., Topology, Academic Press, New York, 1966 | MR | Zbl

[8] Nuray F., Rhoades B. E., “Statistical convergence of sequences of sets”, Fasc. Math., 49 (2012), 87–99 (118991448) | MR | Zbl

[9] Salinetti G., Wets R. J.-B., “On the convergence of sequences of convex sets in finite dimensions”, SIAM Rev., 21:1 (1979), 18–33 | DOI | MR | Zbl

[10] Talo Ö., Sever Y., Başar F., “On statistically convergent sequences of closed sets”, Filomat, 30:6 (2016), 1497–1509 | DOI | MR | Zbl

[11] Ulusu U., Gülle E., “Some statistical convergence types of order $\alpha $ for double set sequences”, Facta Univ. Ser. Math. Inform., 35:3 (2020), 595–603 | DOI | MR | Zbl

[12] Wijsman R. A., “Convergence of sequences of convex sets, cones and functions”, Bull. Amer. Math. Soc., 70 (1964), 186–188 | DOI | MR | Zbl

[13] Wijsman R. A., “Convergence of sequences of convex sets, cones and functions. II”, Trans. Amer. Math. Soc., 123 (1966), 32–45 | DOI | MR | Zbl