Statistical Approximation Properties of a Generalization of Positive Linear Operators

Reyhan Canatan, Ogün Doğru

Abstract

In the present paper, we introduce a generalization of positive linear operators and obtain its Korovkin type statistical approximation properties. The rates of statistical convergence of this generalization is also obtained by means of modulus of continuity and Lipschitz type maximal functions.Secondly, we construct a bivariate generalization of these operators and investigate the statistical approximation properties. We also get a partial differential equation such that the second moment of our bivariate operators is a particular solution of it. Finally, we obtain a Voronovskaja type formulae via statistical limit.

Keywords

Sequence of positive linear operators, Korovkin theorem for statistical approximation, modulus of continuity, Lipschitz type maximal functions

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