Pointwise estimate for some Durrmeyer type operators
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In the present paper we investigate the behavior of some Durrmeyer type operators Ln(f; x), defined as Ln(f;x) = [수식] where the kernel Kn(x, t) may have different values. We give an estimate of the rate of pointwise convergence of these operators on a Lebesgue point of bounded variation function f defined on the interval [0, 1]. Using analysis techniques instead of probability methods we obtain the rate of pointwise convergence of the operators in question. Here we note that this kind of study is different from the earlier studies on such type of operators and have not been investigated for Durrmeyer type operators.
Abstract
In the present paper we investigate the behavior of some Durrmeyer type operators Ln(f; x), defined as Ln(f;x) = [수식] where the kernel Kn(x, t) may have different values. We give an estimate of the rate of pointwise convergence of these operators on a Lebesgue point of bounded variation function f defined on the interval [0, 1]. Using analysis techniques instead of probability methods we obtain the rate of pointwise convergence of the operators in question. Here we note that this kind of study is different from the earlier studies on such type of operators and have not been investigated for Durrmeyer type operators.
참고문헌 (19)
- O. Agratini, "On the rate of convergence of some integral operators for functions of bounded variation", Studia Sci Math. Hungarica, 42(2), pp.235~252 (2005)
- G. Aniol, "On the rate of pointwise convergence of the Durrmeyer type operators", Approx. Theory and its Appl, 11(2), pp.94~105 (1995)
- R. Bojani´c, "On the rate of convergence of Fourier- Legendre series of functions of bounded variation", J. Approx. Theory, 31(1), pp.67~79 (1981)
- P. L. Butzer, "Fourier Analysis and Approximation. Volume 1: One-dimensional theory. Pure and Applied Mathematics", Academic Press New York-London, 40, pp.xvi+553~ (1971)
- F. Chˆeng, "On the rate of convergence of Bernstein polynomials of functions of bounded variation", J. Approx. Theory, 39(3), pp.259~274 (1983)
- par des polynomes de Bernstein modifies, "J Approx Theory", 1981, 325~343
- J. L. Durrmeyer, "Une formule d’inversion de la transformee de Laplace: Application a la Theorie des Moments" (1967), These de 3e cycle, Faculte des Sciences de l’ Universite de Paris
- S. Guo, "On the rate of convergence of Durrmeyer operator for function of bounded variation", J. Approx. Theory, 51, pp.183~192 (1987)
- M. K. Gupta, "note on the Bezier variant of certain Bernstein polynomials", J. Inequalities Pure Applied Mathematics, 6(3), pp.Art 74~ (2005)
- V. Gupta, "A note on the rate of convergence of Durrmeyer type operators for functions of bounded variation", Soochow J. Math, 23(1), pp.115~118 (1997)
- V. Gupta, "On simultaneous approximation for some Bernstein type operators", International J. Math and Math Sci, 2004(71), pp.3951~3958 (2004)
- V. Gupta, "Bezier variant of a new Durrmeyer type operators", Rivista di Matematica della Universit`a di Parma, 7(2), pp.9~21 (2003)
- V. Gupta, "Rate of approximation for certain Durrmeyer operators", Georgian Math J, 13(2), pp.277~284 (2006)
- H. Karsli, "Convergence and rate of convergence by nonlinear singular integral operators depending on two parameters", Appl. Anal, 85(6-7,), pp.781~791 (2006)
- H. Karsli, "Approximation properties of convolution type singular integral operators depending on two parameters and of their derivatives in L1 < a, b >", Proc. 16th Int. Conf. Jangjeon Math. Soc, 16, pp.66~76 (2005)
- H. Karsli, "Rate of convergence of nonlinear integral operators for functions of bounded variation", Calcolo, 45(2), pp.87~98 (2008)
- H. Karsli, "Rate of pointwise convergence of a new kind of gamma operators for functions of bounded variation" (2008), Appl. Math. Lett. in press
- A. Lupas, "Die Folge Der Betaoperatoren, Dissertation", Stuttgart Universit ¨at (1972)
- X. M. Zeng, "On the rate of convergence of the generalized Durrmeyer", J. Approx. Theory 102