In this note we give the Voronovskaya theorem for some linear positive operators of the Szasz-Mirakjan type defined in the space of functions continuous on [0,+∞) and having the exponential growth at infinity. Some approximation properties of these operators are given in [3], [4].
In this paper we extend the Duman-King idea of approximation of functions by positive linear operators preserving , . Using a modification of certain operators preserving and , we introduce operators which preserve and and next we define operators for -times differentiable functions. We show that and have better approximation properties than and .
This paper is motivated by Kirov results on generalized Bernstein polynomials given in (Kirov, G. H., A generalization of the Bernstein polynomials, Math. Balk. New Ser. bf 6 (1992), 147–153.). We introduce certain modified Meyer-König and Zeller operators in the space of differentiable functions of two variables and we study approximation properties for them. Some approximation properties of the Meyer-König and Zeller operators of differentiable functions of one variable are given in (Rempulska,...
We consider the Picard operators and in exponential weighted spaces. We give some elementary and approximation properties of these operators.
In this note we give some direct and inverse approximation theorems for the Picard singular integral in the exponential weighted spaces and some generalized Hölder spaces.
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