Approximation by a Complex Post-Widder Type Operator

Abstract

In the present article, we deal with the so-called overconvergence phenomenon in C of a slightly modified Post-Widder operator of real variable, that is with the extension of its approximation properties from the real axis in the complex plane. In this sense, error estimates in approximation and a quantitative Voronovskaya-type asymptotic formula are established.

Approximation by an Exponential-Type Complex Operators

“…Particular cases of the exponential-type operators studied in the real case in [11], are the Bernstein polynomials, the operators of Szász, of Post-Widder, of Gauss-Weierstrass, of Baskakov, to mention only a few. In the complex variable case, only the approximation properties of the operators of Bernstein, Szász, Baskakov and Post-Widder were already studied, see, e.g., [5,7,9]. It remains as open question to use the method in this paper for other complex exponential-type operators, too.…”