Displaying similar documents to “Approximation and shape preserving properties of the nonlinear Bleimann-Butzer-Hahn operators of max-product kind”

On approximation of functions by certain operators preserving x 2

Lucyna Rempulska, Karolina Tomczak (2008)

Commentationes Mathematicae Universitatis Carolinae

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In this paper we extend the Duman-King idea of approximation of functions by positive linear operators preserving e k ( x ) = x k , k = 0 , 2 . Using a modification of certain operators L n preserving e 0 and e 1 , we introduce operators L n * which preserve e 0 and e 2 and next we define operators L n ; r * for r -times differentiable functions. We show that L n * and L n ; r * have better approximation properties than L n and L n ; r .

A Korovkin type approximation theorems via ℐ -convergence

Oktay Duman (2007)

Czechoslovak Mathematical Journal

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Using the concept of ℐ -convergence we provide a Korovkin type approximation theorem by means of positive linear operators defined on an appropriate weighted space given with any interval of the real line. We also study rates of convergence by means of the modulus of continuity and the elements of the Lipschitz class.