Skip to main content
Log in

Approximation by q Baskakov-Beta-Stancu operators

  • Published:
Rendiconti del Circolo Matematico di Palermo Aims and scope Submit manuscript

Abstract

In the present paper we propose the q analogue of the Baskakov-Beta-Stancu operators. We establish some direct results in the polynomial weighted space of continuous functions defined on the interval [0,∞). In the end, we propose an open problem on Srivastava-Gupta operators.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

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

    Article  MathSciNet  MATH  Google Scholar 

  2. De Sole, A., Kac, V.G.: On integral representations of q-gamma and q-betta functions. Rend. Mat. Accad. Lincei 9(16), 1, 11–29 (2005)

    Google Scholar 

  3. De Vore, R.A., Lorentz, G.G.: Constructive Approximation. Springer, Berlin (1993)

    Google Scholar 

  4. Gadzhiev, A.D.: Theorems of the type of P.P. Korovkin type theorems. Mat. Zametki 20(5), 781–786 (1976). English Translation, Math. Notes 20(5–6), 996–998 (1976)

    MathSciNet  MATH  Google Scholar 

  5. Gasper, G., Rahman, M.: Basic Hypergeometrik Series. Encyclopedia of Mathematics and Its Applications, vol. 35. Cambridge University Press, Cambridge (1990)

    Google Scholar 

  6. Gupta, V.: A note on modified Baskakov type operators. Approx. Theory Appl. 10(3), 74–78 (1994)

    MathSciNet  MATH  Google Scholar 

  7. Gupta, V.: Some approximation properties on q-Durrmeyer operators. Appl. Math. Comput. 197(1), 172–178 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  8. Gupta, V.: A note on q Baskakov-Szasz operators. Lobachevskii J. Math. 31(4), 359–366 (2010)

    Article  MathSciNet  Google Scholar 

  9. Gupta, V.: On certain type Durrmeyer type q Baskakov operators. Ann. Univ. Ferrara 56(2), 295–303 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  10. Gupta, V., Aral, A.: Convergence of the q analogue of Szasz-Beta operators. Appl. Math. Comput. 216, 374–380 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  11. Gupta, V., Aral, A.: Approximation by q Baskakov beta operators. Acta Math. Appl. Sin., Engl. Ser. 27(4), 569–580 (2011)

    Article  MathSciNet  Google Scholar 

  12. Gupta, V., Kim, T.: On the rate of convergence for q modified beta operators. J. Math. Anal. Appl. 377, 471–480 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  13. Gupta, V., Sharma, H.: Recurrence formula and better approximation for q Durrmeyer operators. Lobachevskii J. Math. 32(2), 140–145 (2011)

    Article  MathSciNet  Google Scholar 

  14. Gupta, V., Wang, H.: The rate of convergence of q-Durrmeyer operators for 0<q<1. Math. Methods Appl. Sci. 31(16), 1946–1955 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  15. Ispir, N., Yuksel, I.: On the Bezier variant of Srivastava-Gupta operators. Appl. Math. E Notes 5, 129–137 (2005)

    MathSciNet  MATH  Google Scholar 

  16. Jackson, F.H.: On a q-definite integrals. Q. J. Pure Appl. Math. 41, 193–203 (1910)

    MATH  Google Scholar 

  17. Kac, V.G., Cheung, P.: Quantum Calculus. Universitext. Springer, New York (2002)

    Book  MATH  Google Scholar 

  18. Kim, T.: q-generalized Euler numbers and polynomials. Russ. J. Math. Phys. 13(3), 293–298 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  19. Kim, T.: q-Bernoulli numbers and polynomials associated with Gaussian binomial coefficients. Russ. J. Math. Phys. 15(1), 51–57 (2008)

    MathSciNet  MATH  Google Scholar 

  20. Kim, T.: Some identities on the q-integral representation of the product of several q-Bernstein-type polynomials. Abstr. Appl. Anal. 2011, 634675 (2011), 11 pages

    Google Scholar 

  21. Koornwinder, T.H.: q-special functions, a tutorial. In: Gerstenhaber, M., Stasheff, J. (eds.) Deformation Theory and Quantum Groups with Applications to Mathematical Physics. Contemp. Math., vol. 134. Amer. Math. Soc., Providence (1992)

    Google Scholar 

  22. Li, W.: The Voronovskaja type expansion formula of the modified Baskakov-Beta operators. J. Baoji Univ. Arts Sci., Nat. Sci. 25(2), 94–97 (2005)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Prerna Maheshwari.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Maheshwari, P., Sharma, D. Approximation by q Baskakov-Beta-Stancu operators. Rend. Circ. Mat. Palermo 61, 297–305 (2012). https://doi.org/10.1007/s12215-012-0090-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12215-012-0090-6

Keywords

Mathematics Subject Classification

Navigation