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)
Lacunary statistical convergence of double sequences. (English) Zbl 1106.40002

A. R. Freedman, J. J. Sember and M. Raphael [Proc. Lond. Math. Soc., III. Ser. 37, 508–520 (1978; Zbl 0424.40008)] presented a definition for lacunary refinement as follows: ρ={k ¯ r } is called a lacunary refinement of the lacunary sequence θ={k r } if {k r }{k ¯ r }. They use this definition to present a one-side inclusion with respect to the refined and nonrefined sequence. J. Li [Int. J. Math. Math. Sci. 23, 175–180 (2000; Zbl 0952.40001)] presented the other side of the inclusion.

In this paper, the authors present a multidimensional analogue to the notion of refinement of lacunary sequences, and use this definition to present both sides of the above inclusion. In addition, the authors present a notion of double lacunary statistically Cauchy convergence and use this definition to establish that it is equivalent to the S θr,s -P-convergence. For details, we refer the reader to the paper.

MSC:
40A05Convergence and divergence of series and sequences
40G05Cesàro, Euler, Nörlund and Hausdorff methods
40C05Matrix methods in summability