Research Article
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Year 2021, , 20 - 29, 29.04.2021
https://doi.org/10.47087/mjm.900156

Abstract

References

  • S. Aytar, Rough statistical convergence, Numerical Functional Analysis Optimization \textbf{29(3)} (2008) 291-303.
  • A. Esi, On some triple almost lacunary sequence spaces defined by Orlicz functions, Research and Reviews: Discrete Mathematical Structures \textbf{1(2)} (2014) 16-25.
  • A. Esi and M. Necdet Catalbas, Almost convergence of triple sequences, Global Journal of Mathematical Analysis \textbf{2(1)} (2014) 6-10.
  • A. Esi and E. Savas, On lacunary statistically convergent triple sequences in probabilistic normed space, Appl. Math. and Inf. Sci. \textbf{9(5)} (2015) 2529-2534.
  • A. Esi, S. Araci and M. Acikgoz, Statistical convergence of Bernstein operators, Appl. Math. and Inf. Sci. \textbf{10(6)} (2016) 2083-2086.
  • A. J. Dutta, A. Esi and B. C. Tripathy, Statistically convergent triple sequence spaces defined by Orlicz function, Journal of Mathematical Analysis \textbf{4(2)} (2013) 16-22.
  • A. Esi, S. Araci and Ayten Esi, $\lambda$-statistical convergence of Bernstein polynomial sequences, Advances and Applications in Mathematical Sciences \textbf{16(3)} (2017) 113-119.
  • A. Esi, N. Subramanian and Ayten Esi, On triple sequence space of Bernstein operator of rough $I_{\lambda}$-convergence pre-Cauchy sequences, Proyecciones Journal of Mathematics \textbf{36(4)} (2017) 567-587.
  • S. Debnath, B. Sarma and B. C. Das, Some generalized triple sequence spaces of real numbers, Journal of Nonlinear Analysis and Optimization \textbf{6(1)} (2015) 71-79.
  • S. K. Pal, D. Chandra and S. Dutta, Rough ideal convergence, Hacettepe Journal Mathematics and Statistics \textbf{42(6)} (2013) 633-640.
  • H. X. Phu, Rough convergence in normed linear spaces, Numerical Functional Analysis Optimization \textbf{22} (2001) 201-224.
  • A. Sahiner, M. Gurdal and F. K. Duden, Triple sequences and their statistical convergence, Selcuk J. Appl. Math. \textbf{8(2)} (2007) 49-55.
  • A. Sahiner, B. C. Tripathy, Some $I$-related properties of triple sequences, Selcuk J. Appl. Math. \textbf{9(2)} (2008) 9-18.
  • N. Subramanian and A. Esi, The generalized tripled difference of $\chi^{3}$ sequence spaces, Global Journal of Mathematical Analysis \textbf{3(2)} (2015) 54-60.

On $\left( p,q\right) $-analog of Stancu operators of rough $\lambda$- statistically $\rho$-Cauchy convergence of triple sequence spaces

Year 2021, , 20 - 29, 29.04.2021
https://doi.org/10.47087/mjm.900156

Abstract

In this work, using the concept of natural density, we introduce the $\left(
p,q\right) $-analogue of the Stancu-beta operators of rough $\lambda$%
-statistically $\rho$-Cauchy convergence on triple sequence spaces. We define
the set of Bernstein Stancu beta opeators of rough statistical limit points of
a triple sequence spaces and obtain to $\lambda-$statistical convergence
criteria associated with this set. Also, we examine the relations between the
set of Bernstein-Stancu beta operators of rough $\lambda$-statistically
$\rho$-Cauchy convergence of triple sequences.

References

  • S. Aytar, Rough statistical convergence, Numerical Functional Analysis Optimization \textbf{29(3)} (2008) 291-303.
  • A. Esi, On some triple almost lacunary sequence spaces defined by Orlicz functions, Research and Reviews: Discrete Mathematical Structures \textbf{1(2)} (2014) 16-25.
  • A. Esi and M. Necdet Catalbas, Almost convergence of triple sequences, Global Journal of Mathematical Analysis \textbf{2(1)} (2014) 6-10.
  • A. Esi and E. Savas, On lacunary statistically convergent triple sequences in probabilistic normed space, Appl. Math. and Inf. Sci. \textbf{9(5)} (2015) 2529-2534.
  • A. Esi, S. Araci and M. Acikgoz, Statistical convergence of Bernstein operators, Appl. Math. and Inf. Sci. \textbf{10(6)} (2016) 2083-2086.
  • A. J. Dutta, A. Esi and B. C. Tripathy, Statistically convergent triple sequence spaces defined by Orlicz function, Journal of Mathematical Analysis \textbf{4(2)} (2013) 16-22.
  • A. Esi, S. Araci and Ayten Esi, $\lambda$-statistical convergence of Bernstein polynomial sequences, Advances and Applications in Mathematical Sciences \textbf{16(3)} (2017) 113-119.
  • A. Esi, N. Subramanian and Ayten Esi, On triple sequence space of Bernstein operator of rough $I_{\lambda}$-convergence pre-Cauchy sequences, Proyecciones Journal of Mathematics \textbf{36(4)} (2017) 567-587.
  • S. Debnath, B. Sarma and B. C. Das, Some generalized triple sequence spaces of real numbers, Journal of Nonlinear Analysis and Optimization \textbf{6(1)} (2015) 71-79.
  • S. K. Pal, D. Chandra and S. Dutta, Rough ideal convergence, Hacettepe Journal Mathematics and Statistics \textbf{42(6)} (2013) 633-640.
  • H. X. Phu, Rough convergence in normed linear spaces, Numerical Functional Analysis Optimization \textbf{22} (2001) 201-224.
  • A. Sahiner, M. Gurdal and F. K. Duden, Triple sequences and their statistical convergence, Selcuk J. Appl. Math. \textbf{8(2)} (2007) 49-55.
  • A. Sahiner, B. C. Tripathy, Some $I$-related properties of triple sequences, Selcuk J. Appl. Math. \textbf{9(2)} (2008) 9-18.
  • N. Subramanian and A. Esi, The generalized tripled difference of $\chi^{3}$ sequence spaces, Global Journal of Mathematical Analysis \textbf{3(2)} (2015) 54-60.
There are 14 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Arulmani Indumathı 0000-0003-3249-6525

Ayhan Esi 0000-0003-3137-3865

Nagarajan Subramanian 0000-0002-5895-673X

Mustafa Kemal Özdemir 0000-0001-6798-1868

Publication Date April 29, 2021
Acceptance Date April 12, 2021
Published in Issue Year 2021

Cite

APA Indumathı, A., Esi, A., Subramanian, N., Özdemir, M. K. (2021). On $\left( p,q\right) $-analog of Stancu operators of rough $\lambda$- statistically $\rho$-Cauchy convergence of triple sequence spaces. Maltepe Journal of Mathematics, 3(1), 20-29. https://doi.org/10.47087/mjm.900156
AMA Indumathı A, Esi A, Subramanian N, Özdemir MK. On $\left( p,q\right) $-analog of Stancu operators of rough $\lambda$- statistically $\rho$-Cauchy convergence of triple sequence spaces. Maltepe Journal of Mathematics. April 2021;3(1):20-29. doi:10.47087/mjm.900156
Chicago Indumathı, Arulmani, Ayhan Esi, Nagarajan Subramanian, and Mustafa Kemal Özdemir. “On $\left( p,q\right) $-Analog of Stancu Operators of Rough $\lambda$- Statistically $\rho$-Cauchy Convergence of Triple Sequence Spaces”. Maltepe Journal of Mathematics 3, no. 1 (April 2021): 20-29. https://doi.org/10.47087/mjm.900156.
EndNote Indumathı A, Esi A, Subramanian N, Özdemir MK (April 1, 2021) On $\left( p,q\right) $-analog of Stancu operators of rough $\lambda$- statistically $\rho$-Cauchy convergence of triple sequence spaces. Maltepe Journal of Mathematics 3 1 20–29.
IEEE A. Indumathı, A. Esi, N. Subramanian, and M. K. Özdemir, “On $\left( p,q\right) $-analog of Stancu operators of rough $\lambda$- statistically $\rho$-Cauchy convergence of triple sequence spaces”, Maltepe Journal of Mathematics, vol. 3, no. 1, pp. 20–29, 2021, doi: 10.47087/mjm.900156.
ISNAD Indumathı, Arulmani et al. “On $\left( p,q\right) $-Analog of Stancu Operators of Rough $\lambda$- Statistically $\rho$-Cauchy Convergence of Triple Sequence Spaces”. Maltepe Journal of Mathematics 3/1 (April 2021), 20-29. https://doi.org/10.47087/mjm.900156.
JAMA Indumathı A, Esi A, Subramanian N, Özdemir MK. On $\left( p,q\right) $-analog of Stancu operators of rough $\lambda$- statistically $\rho$-Cauchy convergence of triple sequence spaces. Maltepe Journal of Mathematics. 2021;3:20–29.
MLA Indumathı, Arulmani et al. “On $\left( p,q\right) $-Analog of Stancu Operators of Rough $\lambda$- Statistically $\rho$-Cauchy Convergence of Triple Sequence Spaces”. Maltepe Journal of Mathematics, vol. 3, no. 1, 2021, pp. 20-29, doi:10.47087/mjm.900156.
Vancouver Indumathı A, Esi A, Subramanian N, Özdemir MK. On $\left( p,q\right) $-analog of Stancu operators of rough $\lambda$- statistically $\rho$-Cauchy convergence of triple sequence spaces. Maltepe Journal of Mathematics. 2021;3(1):20-9.

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