Statistically convergent double sequences

By B. Tripathy. 2003

220 citations recorded by the source corpus.

In this aricle we introduce the notion of density of subsets of $ N \times N $. Using this concept we introduce the notion of statistically convergent double sequences and statistically Cauchy double sequences. The decomposition theorem is proved. The inclusion relations are obtained. We have shown that the bounded statistically convergent in Pringsheim's sense sequence space is not separable. A relation between strongly $ p $-Cesaro summability of double sequences and bounded statistically convergent double sequences is established.

Subfields: Mathematical Physics, Numerical Analysis, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/c34534b9a62d7a4cfec04e26eb28da09183743ff

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mathematical Physics

1. B. Tripathy
2. B. Sarma
3. Ahmet Sahiner
4. M. Maity
5. Prasanta Malik
6. Mehmet Gürdal
7. Bipan Hazarika

In Numerical Analysis

1. B. Sarma
2. Ahmet Sahiner
3. Prasanta Malik
4. M. Maity
5. Mehmet Gürdal
6. B. Tripathy

In Statistics and Probability

1. B. Sarma
2. B. Tripathy
3. Ahmet Sahiner
4. M. Maity
5. Prasanta Malik
6. Mehmet Gürdal
7. Bipan Hazarika
8. B. Choudhary

Citations in the corpus

• On rough statistical convergence of double sequences in normed linear spaces (2016, background): “More investigation and applications of statistical convergence of double sequences can be found in [3, 23] and many others.”
• On I-Convergent Double Sequences of Fuzzy Real Numbers (2012, background): “Different classes of sequences of fuzzy numbers have been investigated by Altin, Et and Basarir [1], Altin, Mursaleen and Altinok [2], Altinok, Colak and Et [3], Colak, Altinok and Et [6], Tripathy and Baruah ([15], [16]), Tripathy and Borgohain [17], Tripathy and Dutta ([19], [20]) and many others.”
• STATISTICALLY CONVERGENT DOUBLE SEQUENCE SPACES DEFINED BY ORLICZ FUNCTION (2006, background): “Later on it was studied by Fridy and Orhan [8], Maddox [10], Salat [16], Rath and Tripathy [15], Tripathy [19, 20] and many others.”
• Extremal I-Limit Points Of Double Sequences (2008, background): “Then I2 (ρ) is an admissible ideal in N × N and I2 (ρ) convergence coincides with the statistical convergence in Pringsheim’s sense [12].”