Abstract
The Meyer-Konig and Zeller operator is one of the most challenging operators. Sometimes the study of its properties will rely on the weighted approximation by Baskakov operator. In this paper, this relation is extended to complex space; the quantitative estimates and the Voronovskaja type results for analytic functions by complex Meyer-Konig and Zeller operators were obtained.
Highlights
The well known Meyer-König and Zeller operators are defined for functions f ( x) ∈ C [0,1) by [1]-[7] Mn ( f, x) = ∞ ∑ k =0 f n k +k mn,k (x), wher= e mn,k ( x) n + k k xk
Sometimes the study of its properties will rely on the weighted approximation by Baskakov operator
This relation is extended to complex space; the quantitative estimates and the Voronovskaja type results for analytic functions by complex Meyer-König and Zeller operators were obtained
Summary
The well known Meyer-König and Zeller operators are defined for functions f ( x) ∈ C [0,1) by [1]-[7]. We will obtain the following estimates for the complex Meyer-König and Zeller operators. { } = here f r sup f ( z) : z ∈ Dr. The paper is organized as the following: In Section 2, we are going to promote the relationship between the Meyer-König and Zeller and Baskakov operators to complex space. 2. The Connection between the Complex Meyer-König and Zeller and Baskakov Operators. From the definition of the mapping τ (2) and the operator Υ (4), combining the Proposition 1, we get the mapping τ : Fw → Fw1 is a linear correspondence. The following proposition is very important, it gives the connection between the complex Meyer-König and Zeller operators and the complex Baskakov operators.
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