On the (p,q)-Stancu Generalization of a Genuine Baskakov-Durrmeyer Type Operators

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Ä°smet Yüksel, Ãœlkü 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.

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Ä°smet Yüksel, Ãœlkü Dinlemez Kantar, Birol Altın

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, Ë™ I. Yüksel and B. Altin, 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.