Abstract
Very recently Gupta (Appl. Math. Comput. 197(1), 172–178, 2008) introduced the q-Durrmeyer operators D n,q f and studied some approximation properties of such operators. In the present paper, we extend the studies and here we obtain some local and global direct results for the q-Durrmeyer type operators. Furthermore, we establish a simultaneous approximation theorem for D n,q f, where f is a polynomial.
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References
DeVore, R.A., Lorentz, G.G.: Constructive Approximation. Springer, Berlin (1993)
Ditzian, Z., Totik, V.: Moduli of Smoothness. Springer, New York (1987)
Gupta, V.: Some approximation properties of q-Durrmeyer operators. Appl. Math. Comput. 197(1), 172–178 (2008)
Lee, S.L., Phillips, G.M.: Polynomial interpolation at points of a geometric mesh on a triangle. Proc. R. Soc. Edinb. A 108, 75–87 (1988)
Phillips, G.M.: Bernstein polynomials based on the q-integers. Ann. Numer. Math. 4, 511–518 (1997)
Phillips, G.M.: On generalized Bernstein polynomials. In: Griffiths, D.F., Watson, G.A. (eds.) Numerical Analysis A.R. Mitchell 75th Birthday Volume, pp. 263–269. World Scientific, Singapore (1990)
Wang, H.: Voronovskaya-type formulas and saturation of convergence for q-Bernstein polynomials for 0<q<1. J. Approx. Theory 145, 182–195 (2007)
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Finta, Z., Gupta, V. Approximation by q-Durrmeyer operators. J. Appl. Math. Comput. 29, 401–415 (2009). https://doi.org/10.1007/s12190-008-0141-5
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DOI: https://doi.org/10.1007/s12190-008-0141-5