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

Tuncer Acar; Mohammad Mursaleen; S. A. Mohiuddine

Research Article

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

Year 2018, Volume: 67 Issue: 1, 116 - 128, 01.02.2018

Tuncer Acar Mohammad Mursaleen S. A. Mohiuddine

Abstract

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.

Keywords

(p.q)-integers, Szász-Mirakyan operators, weighted approximation

References

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.

Year 2018, Volume: 67 Issue: 1, 116 - 128, 01.02.2018

Tuncer Acar Mohammad Mursaleen S. A. Mohiuddine

Abstract

References

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.

There are 20 citations in total.

Details

Primary Language	English
Subjects	Mathematical Sciences
Journal Section	Research Articles
Authors	Tuncer Acar Mohammad Mursaleen S. A. Mohiuddine
Publication Date	February 1, 2018
Submission Date	December 26, 16
Acceptance Date	April 3, 2017
Published in Issue	Year 2018 Volume: 67 Issue: 1

Cite

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. February 2018;67(1):116-128.
Chicago	Acar, Tuncer, Mohammad Mursaleen, and S. A. Mohiuddine. “Stancu Type (p,q)-Szász-Mirakyan-Baskakov Operators”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 67, no. 1 (February 2018): 116-28.
EndNote	Acar T, Mursaleen M, Mohiuddine SA (February 1, 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, and S. A. Mohiuddine, “Stancu Type (p,q)-Szász-Mirakyan-Baskakov operators”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 67, no. 1, pp. 116–128, 2018.
ISNAD	Acar, Tuncer et al. “Stancu Type (p,q)-Szász-Mirakyan-Baskakov Operators”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 67/1 (February 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 et al. “Stancu Type (p,q)-Szász-Mirakyan-Baskakov Operators”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 67, no. 1, 2018, pp. 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.