The (p; q)-Bernstein-Stancu operator of rough statistical convergence on triple sequence
DOI:
https://doi.org/10.5269/bspm.v38i7.45791Resumo
In the paper, we investigate rough statistical approximation properties of (p; q)-analogue of Bernstein-Stancu Operators. We study approximation properties based on rough statistical convergence. We also study error bound using modulus of continuity.
Referências
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https://doi.org/10.1080/01630560802001064
2. A. Esi, On some triple almost lacunary sequence spaces defined by Orlicz functions, Research and Reviews: Discrete Mathematical Structures, 1(2), 16-25, (2014).
3. A. Esi and M. Necdet Catalbas, Almost convergence of triple sequences, Global Journal of Mathematical Analysis, 2(1), 6-10, (2014). https://doi.org/10.14419/gjma.v2i1.1709
4. A. Esi and E. Savas, On lacunary statistically convergent triple sequences in probabilistic normed space, Appl. Math. Inf. Sci., 9(5), 2529-2534, (2015).
5. A. Esi, S. Araci and M. Acikgoz, Statistical Convergence of Bernstein Operators, Appl. Math. Inf. Sci., 10(6), 2083-2086, (2016). https://doi.org/10.18576/amis/100610
6. A. J. Datta, A. Esi and B. C. Tripathy, Statistically convergent triple sequence spaces defined by Orlicz function, J. Math. Anal., 4(2), 16-22, (2013).
7. S. Debnath, B. Sarma and B. C. Das, Some generalized triple sequence spaces of real numbers, J. Nonlinear Anal. Optim., 6(1), 71-79, (2015).
8. M. Mursaleen, Khursheed J. Ansari and Asif Khan, Some approximation results by (p,q)-analogue of Bernstein-Stancu operators, Appl. Math. Comput., 264, 392-402, (2015). https://doi.org/10.1016/j.amc.2015.03.135
9. S. K. Pal, D. Chandra and S. Dutta, Rough ideal Convergence, Hacet. J. Math. Stat., 42(6), 633-640, (2013).
10. H. X. Phu, Rough convergence in normed linear spaces, Numer. Funct. Anal. Optim., 22, 201-224, (2001).
11. A. Sahiner, M. Gurdal and F. K. Duden, Triple sequences and their statistical convergence, Sel¸cuk J. Appl. Math., 8(2), 49-55, (2007).
12. A. Sahiner and B. C. Tripathy, Some Irelated properties of triple sequences, Selcuk J. Appl. Math., 9(2), 9-18, (2008).
13. N. Subramanian and A. Esi, The generalized tripled difference of 3 sequence spaces, Global Journal of Mathematical Analysis, 3(2), 54-60, (2015). https://doi.org/10.14419/gjma.v3i2.4412
14. A. Esi, M. Kemal Ozdemir and N. Subramanian, The (p, q)-Bernstein-Stancu operator of rough statistical convergence on triple sequence, ICMS (2018), Maltepe, Turkey.
https://doi.org/10.1080/01630560802001064
2. A. Esi, On some triple almost lacunary sequence spaces defined by Orlicz functions, Research and Reviews: Discrete Mathematical Structures, 1(2), 16-25, (2014).
3. A. Esi and M. Necdet Catalbas, Almost convergence of triple sequences, Global Journal of Mathematical Analysis, 2(1), 6-10, (2014). https://doi.org/10.14419/gjma.v2i1.1709
4. A. Esi and E. Savas, On lacunary statistically convergent triple sequences in probabilistic normed space, Appl. Math. Inf. Sci., 9(5), 2529-2534, (2015).
5. A. Esi, S. Araci and M. Acikgoz, Statistical Convergence of Bernstein Operators, Appl. Math. Inf. Sci., 10(6), 2083-2086, (2016). https://doi.org/10.18576/amis/100610
6. A. J. Datta, A. Esi and B. C. Tripathy, Statistically convergent triple sequence spaces defined by Orlicz function, J. Math. Anal., 4(2), 16-22, (2013).
7. S. Debnath, B. Sarma and B. C. Das, Some generalized triple sequence spaces of real numbers, J. Nonlinear Anal. Optim., 6(1), 71-79, (2015).
8. M. Mursaleen, Khursheed J. Ansari and Asif Khan, Some approximation results by (p,q)-analogue of Bernstein-Stancu operators, Appl. Math. Comput., 264, 392-402, (2015). https://doi.org/10.1016/j.amc.2015.03.135
9. S. K. Pal, D. Chandra and S. Dutta, Rough ideal Convergence, Hacet. J. Math. Stat., 42(6), 633-640, (2013).
10. H. X. Phu, Rough convergence in normed linear spaces, Numer. Funct. Anal. Optim., 22, 201-224, (2001).
11. A. Sahiner, M. Gurdal and F. K. Duden, Triple sequences and their statistical convergence, Sel¸cuk J. Appl. Math., 8(2), 49-55, (2007).
12. A. Sahiner and B. C. Tripathy, Some Irelated properties of triple sequences, Selcuk J. Appl. Math., 9(2), 9-18, (2008).
13. N. Subramanian and A. Esi, The generalized tripled difference of 3 sequence spaces, Global Journal of Mathematical Analysis, 3(2), 54-60, (2015). https://doi.org/10.14419/gjma.v3i2.4412
14. A. Esi, M. Kemal Ozdemir and N. Subramanian, The (p, q)-Bernstein-Stancu operator of rough statistical convergence on triple sequence, ICMS (2018), Maltepe, Turkey.
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2019-10-14
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