Title: On the (p,q)−Stancu Generalization of a Genuine Baskakov-Durrmeyer Type Operators
Author(s): İsmet Yüksel, Ülkü Dinlemez Kantar, Birol Altın
Pages: 138-145
Cite as:
İsmet Yüksel, Ülkü Dinlemez Kantar, Birol Altın, On the (p,q)−Stancu Generalization of a Genuine Baskakov-Durrmeyer Type Operators, Int. J. Anal. Appl., 15 (2) (2017), 138-145.

Abstract


In this paper, we introduce a Stancu generalization of a genuine Baskakov-Durrmeyer type operators via (p,q)− integer. We investigate approximation properties of these operators. Furthermore, we study on the linear positive operators in a weighted space of functions and obtain the rate of these convergence using weighted modulus of continuity.


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References


  1. A. Aral and V. Gupta, Generalized q−Baskakov operators, Math. Slovaca 61 (4) (2011), 619–634.

  2. A. Aral, V. Gupta and Agarwal, R. P. , Applications of q-calculus in operator theory. Springer, New York, 2013.

  3. A. Aral and V. Gupta, (p,q)−Type beta functions of second kind, Adv. Oper. Theory 1 (1) (2016), 134-146.

  4. T. Acar, S. A. Mohiuddine and M. Mursaleen, Approximation by (p,q)−Baskakov-Durrmeyer-Stancu Operators, Complex Anal. Oper. Theory DOI 10.1007/s11785-016-0633-5.

  5. P. N. Agrawal and K. J., Approximation of unbounded functions by a new sequence of linear positive operators, J. Math. Anal. Appl. 225 (2) (1998), 660–672.

  6. R. A. Devore and G. G. Lorentz, Constructive Approximation, Springer, Berlin, 1993.

  7. ¨ U. Dinlemez, ˙ I. Yüksel and B. Altın, A note on the approximation by the q-hybrid summation integral type operators, Taiwanese J. Math. 18 (3) (2014), 781–792.

  8. A. D. Gadzhiev, 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.

  9. V. Gupta, (p, q)-Szász–Mirakyan–Baskakov Operators, Complex Anal. Oper. Theory, DOI 10.1007/s11785-015- 0521-4.

  10. M. Mursaleen, K. J. Ansari and A. Khan, On (p,q)-analogue of Bernstein Operators, Appl. Math. Comput., 266 (2015) 874-882.

  11. M. Mursaleen, K. J. Ansari and A. Khan, Some Approximation Results by (p,q)-analogue of Bernstein-Stancu operators, Appl. Math. Comput., 264 (2015) 392-402

  12. [Corrigendum: Appl. Math. Comput, 269 (2015) 744–746].

  13. M. Mursaleen, Md. Nasiruzzaman, A. Khan and K. J. Ansari, Some approximation results on Bleimann-Butzer-Hahn operators defined by (p,q)−integers, Filomat 30 (3) (2016), 639–648.

  14. T. Acar, A. Aral and S. A. Mohiuddine, On Kantorovich modification of (p,q)−Baskakov operators. J. Inequal. Appl., 2016:98 (2016), 14 pp.

  15. A. De Sole and V. G. Kac, On integral representations of q−gamma and q−beta functions. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl. 16 (1) (2005), 11–29.

  16. V. Sahai and S. Yadav, Representations of two parameter quantum algebras and p,q−special functions. J. Math. Anal. Appl. 335 (1) (2007), 268–279.

  17. D. K. Verma, V. Gupta and P. N. Agrawal, Some approximation properties of Baskakov-Durrmeyer-Stancu opera- tors. Appl. Math. Comput. 218 (11) (2012), 6549–6556.