Statistical Approximation Properties of a Generalization of Positive Linear Operators
Keywords:
Sequence of positive linear operators, Korovkin theorem for statistical approximation, modulus of continuity, Lipschitz type maximal functionsAbstract
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.Downloads
Issue
Section
Mathematical Modeling and Numerical Analysis
License
Upon acceptance of an article by the journal, the author(s) accept(s) the transfer of copyright of the article to European Journal of Pure and Applied Mathematics.
European Journal of Pure and Applied Mathematics will be Copyright Holder.
How to Cite
Statistical Approximation Properties of a Generalization of Positive Linear Operators. (2012). European Journal of Pure and Applied Mathematics, 5(1), 75-87. https://www.ejpam.com/index.php/ejpam/article/view/1492