zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Statistical convergence of sequences of sets. (English) Zbl 06174708

In this paper, the authors generalized statistical convergence using Kuratowski convergence, which was introduced in [K. Kuratowski, Topology. Vol. I. New edition, revised and augmented. New York-London: Academic Press; Warszawa: PWN-Polish Scientific Publishers. (1966; Zbl 0158.40802)], Wijsman convergence, which was introduced in [R. A. Wijsman, Bull. Am. Math. Soc. 70, 186–188 (1964; Zbl 0121.39001), Trans. Am. Math. Soc. 123, 32–45 (1966; Zbl 0146.18204)] and Hausdorf convergence, which was introduced in [F. Hausdorff, Grundzüge der Mengenlehre. Mit 53 Figuren im Text. Leipzig: Veit & Comp. (1914; Zbl 45.0123.01)]. They give the definitons of Kuratowski, Wijsman and Hausdorff statistical convergence of sequences of sets. Then they proved the theorem that says, description

[i] {A k } is a Wijsman statistically convergent sequence,

[ii] {A k } is a Wijsman statistically Cauchy sequence,

[iii] {A k } is a sequence for which there is a Wijsman convergent sequence {B k } such that A k =B k almost all k. are equivalent.

Moreover, they give some Tauberian conditions for Wijsman and Hausdorf statistical convergences.

Finally, they introduced Cesàro summable, strongly Cesàro summable, strongly p-Cesàro summable, almost converget, strongly almost convergent and strongly p-almost convergent for above definitions, and then they give some basic theorems of those new notions.

MSC:
40A05Convergence and divergence of series and sequences
46E25Rings and algebras of continuous, differentiable or analytic functions