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Stancu Type (p,q)-Szász-Mirakyan-Baskakov operators

Yıl 2018, Cilt: 67 Sayı: 1, 116 - 128, 01.02.2018

Öz

In the present paper, we introduce Stancu type generalization of (p,q)-Szasz-Mirakyan-Baskakov operators and investigate their approximation properties such as weighted approximation, rate of convergence and pointwise convergence.

Kaynakça

  • Acar, T., (p,q)-generalization of Szász-Mirakyan operators, Math. Method. Appl. Sci., 39 (10), 2016, 2685-2695.
  • Acar, T., Agrawal, P. N. , Kumar, S., On a modification of (p,q)-Szász-Mirakyan operators, Comp. Anal. Oper. Theo., 2016, DOI: 10.1007/s11785-016-0613-9.
  • Acar, T., Aral, A., Mohiuddine, S. A., On Kantorovich modifications of (p,q)-Baskakov operators, J. Inequal. Appl., 2016, 2016:98.
  • Acar, T., Aral, A., Mohiuddine, Approximation by bivariate (p,q)-Bernstein-Kantorovich operators, Iran. J. Sci. Technol. Trans. A Sci., 2016, DOI: 10.1007/s40995-016-0045-4.
  • Acar, T. Gupta, V., Aral, A., Rate of Convergence for Generalized Szász Operators, Bull. Math. Sci., 1 (1), 2011, 99-113.
  • Devore, R. A. , Lorentz, G. G., Constructive Approximation, Springer, Berlin, 1993.
  • Gupta, V., (p,q)-Szász-Mirakyan-Baskakov operators, Complex Anal. Oper. Theory, 2016, DOI: 10.1007/s11785-015-0521-4.
  • Gadzhiev, A. D., Theorems of the type of P. P. Korovkin type theorems, Math. Zametki, 20 (5), 1976 781-786; English Translation, Math Notes 20 (5-6) 1976 996-998.
  • Hounkonnou, M. N., Désiré, J., Kyemba, B., R(p,q)-calculus: differentiation and integration, SUT Journal of Mathematics, 49 (2), 2013, 145-167.
  • Jagannathan, R., Rao, K. S., Two-parameter quantum algebras, twin-basic numbers, and associated generalized hypergeometric series, Proceedings of the International Conference on Number Theory and Mathematical Physics, 20-21 December 2005.
  • Ibikli, E., Gadjieva, E. A., The order of approximation of some unbounded function by the sequences of positive linear operators, Turk. J. Math., 19 (3), 1995, 331-337.
  • Ince Ilarslan, H. G., Acar, T., Approximation by bivariate (p,q)-Baskakov-Kantorovich operators, Georgian Math. J., 2016, DOI: 10.1515/gmj-2016-0057.
  • Lenze, B., On Lipschitz type maximal functions and their smoothness spaces, Nederl. Akad. Indag. Math., 50, 1988 53--63.
  • Mahmodov, N. I., On q-parametric Szász-Mirakjan operators, Mediterr. J. Math., 7, 2010, 297--311.
  • Mursaleen, M., Ansari, K. J., Khan, A., On (p,q)-analogue of Bernstein Operators, Appl. Math. Comput., 266, 2015, 874-882.
  • Mursaleen, M., Ansari, K. J., Khan, A., Some Approximation Results by (p,q)-analogue of Bernstein-Stancu operators, Appl. Math. Comput., 264, 2015, 392-402 [Corrigendum: Appl. Math. Comput, 269 (2015) 744--746].
  • Mursaleen, M., Nasiruzzaman, Md., Khan, A. and Ansari, K. J., Some approximation results on Bleimann-Butzer-Hahn operators defined by (p,q)-integers, Filomat, 30(3), (2016), 639--648.
  • Mursaleen, M., Nasiruzzaman, Md., Nurgali, A., Some approximation results on Bernstein-Schurer operators defined by (p,q)-integers, J. Ineq. Appl., 2015 (2015): 249.
  • Mursaleen, M., Alotaibi, A., Ansari,, K.J., On a Kantorovich variant of (p,q)- Szász-Mirakjan operators, J. Func. Spaces, Volume 2016, Article ID 1035253, 9 pages.
  • Sahai, V., Yadav, S., Representations of two parameter quantum algebras and p,q-special functions, J. Math. Anal. Appl. 335 (2007), 268-279.
Yıl 2018, Cilt: 67 Sayı: 1, 116 - 128, 01.02.2018

Öz

Kaynakça

  • Acar, T., (p,q)-generalization of Szász-Mirakyan operators, Math. Method. Appl. Sci., 39 (10), 2016, 2685-2695.
  • Acar, T., Agrawal, P. N. , Kumar, S., On a modification of (p,q)-Szász-Mirakyan operators, Comp. Anal. Oper. Theo., 2016, DOI: 10.1007/s11785-016-0613-9.
  • Acar, T., Aral, A., Mohiuddine, S. A., On Kantorovich modifications of (p,q)-Baskakov operators, J. Inequal. Appl., 2016, 2016:98.
  • Acar, T., Aral, A., Mohiuddine, Approximation by bivariate (p,q)-Bernstein-Kantorovich operators, Iran. J. Sci. Technol. Trans. A Sci., 2016, DOI: 10.1007/s40995-016-0045-4.
  • Acar, T. Gupta, V., Aral, A., Rate of Convergence for Generalized Szász Operators, Bull. Math. Sci., 1 (1), 2011, 99-113.
  • Devore, R. A. , Lorentz, G. G., Constructive Approximation, Springer, Berlin, 1993.
  • Gupta, V., (p,q)-Szász-Mirakyan-Baskakov operators, Complex Anal. Oper. Theory, 2016, DOI: 10.1007/s11785-015-0521-4.
  • Gadzhiev, A. D., Theorems of the type of P. P. Korovkin type theorems, Math. Zametki, 20 (5), 1976 781-786; English Translation, Math Notes 20 (5-6) 1976 996-998.
  • Hounkonnou, M. N., Désiré, J., Kyemba, B., R(p,q)-calculus: differentiation and integration, SUT Journal of Mathematics, 49 (2), 2013, 145-167.
  • Jagannathan, R., Rao, K. S., Two-parameter quantum algebras, twin-basic numbers, and associated generalized hypergeometric series, Proceedings of the International Conference on Number Theory and Mathematical Physics, 20-21 December 2005.
  • Ibikli, E., Gadjieva, E. A., The order of approximation of some unbounded function by the sequences of positive linear operators, Turk. J. Math., 19 (3), 1995, 331-337.
  • Ince Ilarslan, H. G., Acar, T., Approximation by bivariate (p,q)-Baskakov-Kantorovich operators, Georgian Math. J., 2016, DOI: 10.1515/gmj-2016-0057.
  • Lenze, B., On Lipschitz type maximal functions and their smoothness spaces, Nederl. Akad. Indag. Math., 50, 1988 53--63.
  • Mahmodov, N. I., On q-parametric Szász-Mirakjan operators, Mediterr. J. Math., 7, 2010, 297--311.
  • Mursaleen, M., Ansari, K. J., Khan, A., On (p,q)-analogue of Bernstein Operators, Appl. Math. Comput., 266, 2015, 874-882.
  • Mursaleen, M., Ansari, K. J., Khan, A., Some Approximation Results by (p,q)-analogue of Bernstein-Stancu operators, Appl. Math. Comput., 264, 2015, 392-402 [Corrigendum: Appl. Math. Comput, 269 (2015) 744--746].
  • Mursaleen, M., Nasiruzzaman, Md., Khan, A. and Ansari, K. J., Some approximation results on Bleimann-Butzer-Hahn operators defined by (p,q)-integers, Filomat, 30(3), (2016), 639--648.
  • Mursaleen, M., Nasiruzzaman, Md., Nurgali, A., Some approximation results on Bernstein-Schurer operators defined by (p,q)-integers, J. Ineq. Appl., 2015 (2015): 249.
  • Mursaleen, M., Alotaibi, A., Ansari,, K.J., On a Kantorovich variant of (p,q)- Szász-Mirakjan operators, J. Func. Spaces, Volume 2016, Article ID 1035253, 9 pages.
  • Sahai, V., Yadav, S., Representations of two parameter quantum algebras and p,q-special functions, J. Math. Anal. Appl. 335 (2007), 268-279.
Toplam 20 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Research Article
Yazarlar

Tuncer Acar

Mohammad Mursaleen

S. A. Mohiuddine

Yayımlanma Tarihi 1 Şubat 2018
Gönderilme Tarihi 26 Aralık 16
Kabul Tarihi 3 Nisan 2017
Yayımlandığı Sayı Yıl 2018 Cilt: 67 Sayı: 1

Kaynak Göster

APA Acar, T., Mursaleen, M., & Mohiuddine, S. A. (2018). Stancu Type (p,q)-Szász-Mirakyan-Baskakov operators. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 67(1), 116-128.
AMA Acar T, Mursaleen M, Mohiuddine SA. Stancu Type (p,q)-Szász-Mirakyan-Baskakov operators. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Şubat 2018;67(1):116-128.
Chicago Acar, Tuncer, Mohammad Mursaleen, ve S. A. Mohiuddine. “Stancu Type (p,q)-Szász-Mirakyan-Baskakov Operators”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 67, sy. 1 (Şubat 2018): 116-28.
EndNote Acar T, Mursaleen M, Mohiuddine SA (01 Şubat 2018) Stancu Type (p,q)-Szász-Mirakyan-Baskakov operators. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 67 1 116–128.
IEEE T. Acar, M. Mursaleen, ve S. A. Mohiuddine, “Stancu Type (p,q)-Szász-Mirakyan-Baskakov operators”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 67, sy. 1, ss. 116–128, 2018.
ISNAD Acar, Tuncer vd. “Stancu Type (p,q)-Szász-Mirakyan-Baskakov Operators”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 67/1 (Şubat 2018), 116-128.
JAMA Acar T, Mursaleen M, Mohiuddine SA. Stancu Type (p,q)-Szász-Mirakyan-Baskakov operators. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2018;67:116–128.
MLA Acar, Tuncer vd. “Stancu Type (p,q)-Szász-Mirakyan-Baskakov Operators”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 67, sy. 1, 2018, ss. 116-28.
Vancouver Acar T, Mursaleen M, Mohiuddine SA. Stancu Type (p,q)-Szász-Mirakyan-Baskakov operators. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2018;67(1):116-28.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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