Displaying similar documents to “On the rate of convergence of certain approximation operators.”

On integral type generalizations of positive linear operators

O. Duman, M. A. Özarslan, O. Doğru (2006)

Studia Mathematica

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We introduce a sequence of positive linear operators including many integral type generalizations of well known operators. Using the concept of statistical convergence we obtain some Korovkin type approximation theorems for those operators, and compute the rates of statistical convergence. Furthermore, we deal with the local approximation and the rth order generalization of our operators.

Approximation by the Bézier variant of the MKZ-Kantorovich operators in the case α < 1

Xiao-Ming Zeng, Vijay Gupta (2009)

Open Mathematics

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The pointwise approximation properties of the Bézier variant of the MKZ-Kantorovich operators M ^ n , α ( f , x ) for α ≥ 1 have been studied in [Comput. Math. Appl., 39 (2000), 1-13]. The aim of this paper is to deal with the pointwise approximation of the operators M ^ n , α ( f , x ) for the other case 0 < α < 1. By means of some new techniques and new inequalities we establish an estimate formula on the rate of convergence of the operators M ^ n , α ( f , x ) for the case 0 < α < 1. In the end we propose the q-analogue of...

I-convergence theorems for a class of k-positive linear operators

Mehmet Özarslan (2009)

Open Mathematics

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In this paper, we obtain some approximation theorems for k- positive linear operators defined on the space of analytical functions on the unit disc, via I-convergence. Some concluding remarks which includes A-statistical convergence are also given.