© Hindawi Publishing Corp. RATE OF CONVERGENCE OF BOUNDED VARIATION FUNCTIONS BY A BÉZIER-DURRMEYER VARIANT OF THE BASKAKOV OPERATORS (original) (raw)
Related papers
A Study on the Rate of Convergence of Chlodovsky-Durrmeyer Operator and Their Bézier Variant
In this paper, we have studied the Bézier variant of Chlodovsky-Durrmeyer operators í µí°· í µí± ,í µí¼ for function f measurable and locally bounded on the interval [0,∞). In this we improved the result given by Ibikl E. And Karsli H. [14]. We estimate the rate of pointwise convergence of í µí°· í µí± ,í µí¼ í µí± (í µí±¥) at those í µí±¥ > 0 at which the one-sided limits í µí± í µí±¥ + , í µí±(í µí±¥−) exist by using the Chanturia modulus of variation. In the special case í µí¼ = 1 the recent result of Ibikl E. And Karsli H. [14] concerning the Chlodowsky-Durrmeyer operators í µí°· í µí± is essentially improved and extended to more general classes of functions.
On the rate of convergence of some operators on functions of bounded variation
Journal of Approximation Theory, 1989
Let L,(f; x) denote the Feller operator where f is a function of bounded variation. The rates of convergence are determined by estimating IL,(J x)-f(x)1 in terms of certain bounds. These results extend and sharpen the results of Cheng [J. Approx. Theory 39 (1983), 259-2741 for Bernstein polynomials. Several classical operators are discussed as examples.
A note on rate of approximation for certain Bezier-Durrmeyer operators
МАТЕМАТИЧКИ ВЕСНИК, 2011
Abstract. The present paper deals with certain Bézier-Durrmeyer type sequence of linear positive operators Mn, α (f, x), having different basis functions in summation and integration. We estimate the rate of convergence of these operators Mn, α (f, x), for functions having ...