On the Micchelli combinations of modified beta operators
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In the present paper, we study modified Beta operator with the weight function of Baskakov basis function. We extend the result of [3] and study simultaneous approximation properties of these operators, we estimate the local direct result in terms of modulus of continuity. Here we improve the order of approximation for these operators by applying iterative condition. We also establish an asymptotic formula and error estimate in terms of higher order modulus of continuity in simultaneous approximation for the iterative combinations (see also [9]) of these operators.
Abstract
In the present paper, we study modified Beta operator with the weight function of Baskakov basis function. We extend the result of [3] and study simultaneous approximation properties of these operators, we estimate the local direct result in terms of modulus of continuity. Here we improve the order of approximation for these operators by applying iterative condition. We also establish an asymptotic formula and error estimate in terms of higher order modulus of continuity in simultaneous approximation for the iterative combinations (see also [9]) of these operators.
참고문헌 (9)
- P.N. Agarwal, "Approximation by iterative combinations of a new sequence of linear positive operators, Advances in Constructive Approximation", pp.13~24 (2004), Nashboro Press
- S. Goldberg, "Minimum Moduli of differential operators", Proc. London, Math. Soc, 23, pp.159~180 (1971)
- V. Gupta, "Simultaneous approximation by modified beta operators", Istanbul uni. Fen. Fak. Met. Derg, 54, pp.11~22 (1995)
- V. Gupta, "Lp-Inverse Theorem for Modified Beta operators", International Journal of Mathematics and Mathematical Sciences, 20, pp.1295~1303 (2003)
- M. K. Gupta, "The iterative combinations of a new sequence of linear positive operators", Math Comput Modelling, 39, pp.521~527 (2004)
- P. Maheshwari, "An estimate on the rate of convergence for modified Beta operators", Indian J. of Pure and Appl. Math, 34(6), pp.927~934 (2003)
- P. Maheshwari, "An Inverse Result in Simultaneous approximation Of modified Beta operators", Georgian Mathematical Journal, 13(2), pp.297~306 (2006)
- P.Maheshwari, "Saturation theorem for the combinations of modified Beta operators in Lp spaces", Appl. Math. E-notes, 7, pp.32~37 (2007)
- C.A. Micchelli, "Saturation class and iterates of Bernstein polynomials", J. Approx. Theory, 8, pp.1~8 (1973)