• Chen, Shu-Ni (School of Mathematical Sciences Xiamen University) ;
  • Cheng, Wen-Tao (School of Mathematical Sciences Anqing Normal University) ;
  • Zeng, Xiao-Ming (School of Mathematical Sciences Xiamen University)
  • 투고 : 2014.08.18
  • 발행 : 2017.03.31


In this paper, we propose the Stancu type generalization of a kind of modified q-Gamma operators. We estimate the moments of these operators and give the basic convergence theorem. We also obtain the Voronovskaja type theorem. Furthermore, we obtain the local approximation, rate of convergence and weighted approximation for these operators.


연구 과제 주관 기관 : National Natural Science Foundation of China


  1. A. Aral, V. Gupta, and R. P. Agarwal, Application of q-Calculus in Operator Theory, Springer, 2013.
  2. Q. M. Cai and X. M. Zeng, On the convergence of a kind of a modified q-Gamma operators, J. Comput. Anal. Appl. 15 (2013), no. 5, 826-832.
  3. W. Z. Chen and S. S. Guo, On the rate of convergence of the gamma operator for functions of bounded variation, Approx. Theory Appl. 1 (1985), no. 5, 85-96.
  4. R. A. DeVore and G. G. Lorentz, Construtive Approximation, Springer, Berlin 1993.
  5. Z. Finta and V. Gupta, Approximation properties of q-Baskakov operators, Cent. Eur. J. Math. 8 (2010), no. 1, 199-211.
  6. N. K. Govil and V. Gupta, q-Beta-Szasz-Stancu operators, Adv. Stud. Contemp. Math. 22 (2012), no. 1, 117-123.
  7. V. Gupta and R. P. Agarwal, Convergence Estimates in Approximation Theory. VIII, Springer, New York, 2014.
  8. V. Gupta and T. Kim, On the rate of approximation by q modified beta operators, J. Math. Anal. Appl. 377 (2011), no. 2, 471-480.
  9. V. Gupta and T. Kim, On a q-analog of the Baskakov basis fuctions, Russ. J. Math. Phys. 20 (2013), no. 3, 276-282.
  10. V. Kac and P. Cheung, Quantum Calculus, Universitext, Springer, New York, 2002.
  11. H. Karsli, Rate of convergence of new Gamma type operators for functions with derivatives of bounded variation, Math. Comput. Modelling 45 (2007), no. 5-6, 617-624.
  12. P. P. Korovkin, Linear Operators and Approximation Theory, Hindustan Publ. Corp., India, 1960.
  13. N. I. Mahmudov, On q-parametric Szasz-Mirakjan operators, Mediterr. J. Math. 7 (2010), no. 3, 297-311.
  14. N. I. Mahmudov and P. Sabancigil, q-Parametric Bleimann Butzer and Hahn operators, J. Inequal. Appl. 2008 (2008), Article ID 816377, 15 pp.
  15. G. M. Phillips, Bernstein polynomials based on the q-integers The Heritage of P. L. Chebyshew: A Festschrift in honor of the 70th-birthday of Professor T. J. Rivlin, Ann. Numer. Math. 4 (1997), no. 1-4, 511-518.
  16. D. D. Stancu, Approximation of functions by a new class of linear polynomials operators, Rev. Roumaine Math. Pures Appl. 13 (1968), no. 8, 1173-1194.
  17. V. Totik, The Gamma operators in $L_p$ spaces, Publ. Math. 32 (1985), 43-55.
  18. T. Trif, Meyer-Konig and Zeller operators based on the q-integers, Rev. Anal. Numer. Theor. Approx. 158 (2002), 221-229.
  19. V. S. Videnskii, On some class of q-parametric positive operators, Operator Theory:Advances and Application 158 (2005), 213-222.
  20. X. W. Xu and J. Y. Wang, Approximation properties of modified Gamma opeartos, J. Math. Anal. Appl. 332 (2007), no. 2, 798-813.
  21. I. Yuksel and N. Ispir, Weighted approximation by a certain family of summation integral-type operators, Comput. Math. Appl. 52 (2006), no. 10-11, 1463-1470.
  22. X. M. Zeng, Approximation properties of Gamma opeartos, J. Math. Anal. Appl. 311 (2005), no. 2, 389-401.

피인용 문헌

  1. -Analogue of Gamma Operators vol.2019, pp.2314-8888, 2019,