New perspectives on \(\mathfrak{T}_{2}\)-statistical supremum-infimum for sequences
Authors
R. Savas
- Department of Mathematics and Science Education, Istanbul Medeniyet University, Istanbul, Turkey.
R. Akbıyık
- Department of Mathematics, Bartın University, 74100, Bartın, Turkey.
Ö. Kisi
- Department of Mathematics, Bartın University, 74100, Bartın, Turkey.
Abstract
In recent years, many researchers have made significant contributions to
summability theory by linking various convergence concepts of sequences. In
this work, we present the definitions of \(\mathfrak{I}_{2}\)-statistical
supremum and \(\mathfrak{I}_{2}\)-statistical infimum for sequences, and
investigate some of their key properties. Additionally, we introduce the
concept of \(\mathfrak{I}_{2}\)-statistical monotonicity and establish the
criteria under which an \(\mathfrak{I}_{2}\)-statistically monotonic sequence
converges in the \(\mathfrak{I}_{2}\)-statistical sense. Ultimately, we provide
both a necessary and a sufficient criterion for the \(\mathfrak{I}_{2}%
\)-statistical convergence of a real-valued sequence.
Share and Cite
ISRP Style
R. Savas, R. Akbıyık, Ö. Kisi, New perspectives on \(\mathfrak{T}_{2}\)-statistical supremum-infimum for sequences, Journal of Nonlinear Sciences and Applications, 18 (2025), no. 4, 272--279
AMA Style
Savas R., Akbıyık R., Kisi Ö., New perspectives on \(\mathfrak{T}_{2}\)-statistical supremum-infimum for sequences. J. Nonlinear Sci. Appl. (2025); 18(4):272--279
Chicago/Turabian Style
Savas, R., Akbıyık, R., Kisi, Ö.. "New perspectives on \(\mathfrak{T}_{2}\)-statistical supremum-infimum for sequences." Journal of Nonlinear Sciences and Applications, 18, no. 4 (2025): 272--279
Keywords
- \(\mathfrak{I}_{2}\)-statistical convergencee
- \(\mathfrak{I}_{2}\)-statistical supremum
- \(\mathfrak{I}_{2}\)-statistical infumum
- filter
MSC
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