The goal of this paper is to give a form of the operator involving the generating function of Apostol-Genocchi polynomials of orderα.Applying the Korovkin theorem,we arrive at the convergence of the operator with the...The goal of this paper is to give a form of the operator involving the generating function of Apostol-Genocchi polynomials of orderα.Applying the Korovkin theorem,we arrive at the convergence of the operator with the aid of moments and central moments.We determine the rate of convergence of the operator using several tools such as K-functional,modulus of continuity,second modulus of continuity.We also give a type of Voronovskaya theorem for estimating error.Moreover,we investigate some results about convergence properties of the operator in a weighted space.Finally,we give numerical examples to support our theorems by using the Maple.展开更多
In this present paper, firstly, the modified positive operators and their discrete operators are constructed. Then, we investigate the statistical approximation properties and rates of convergence by using modulus of ...In this present paper, firstly, the modified positive operators and their discrete operators are constructed. Then, we investigate the statistical approximation properties and rates of convergence by using modulus of continuity of these positive linear operators. Finally, we obtain the rate of statistical convergence of truncated operators.展开更多
文摘The goal of this paper is to give a form of the operator involving the generating function of Apostol-Genocchi polynomials of orderα.Applying the Korovkin theorem,we arrive at the convergence of the operator with the aid of moments and central moments.We determine the rate of convergence of the operator using several tools such as K-functional,modulus of continuity,second modulus of continuity.We also give a type of Voronovskaya theorem for estimating error.Moreover,we investigate some results about convergence properties of the operator in a weighted space.Finally,we give numerical examples to support our theorems by using the Maple.
文摘In this present paper, firstly, the modified positive operators and their discrete operators are constructed. Then, we investigate the statistical approximation properties and rates of convergence by using modulus of continuity of these positive linear operators. Finally, we obtain the rate of statistical convergence of truncated operators.
