On Approximation by Post-Widder and Stancu Operators Preserving x²

Abstract

In the papers [5]-[7] was examined approximation of functions by the modified Szász-Mrakyan operators and other positive linear operators preserving e2(x) = x 2. In this paper we introduce the Post-Widder and Stancu operators preserving x 2 in polynomial weighted spaces. We show that these operators have better approximation properties than classical Post-Widder and Stancu operators.

On Sequences of J. P. King-Type Operators

“…Post Widder and Stancu operators are instead object of a modification that preserves 2 in polynomial weighted spaces, proposed by Rempulska and Skorupka in [12]. Also in this case better approximation properties than the original operators are achieved.…”

Approximation by a Complex Post-Widder Type Operator

“…Denoting e i (x) = x i , i = 0,1,2, according to [2], Chapter 9 (see, also [8]) we have Remark 1.1. In the paper [1] (see also [9], pp.…”

Quantitative Global Estimates for Generalized Double Szasz-Mirakjan Operators

“…it has been shown in [2] that the operators defined by * ( ; ) := ( ; V ( )) (6) do not preserve the test functions 1 ( ) = and 2 ( ) = 2 but provide the best error estimation among all the Szász-Mirakjan operators for all ∈ ([0, ∞)) and for each ∈ [1/2, ∞). For the other linear positive operator families which preserve 2 ( ) = 2 , we refer [3][4][5][6][7][8][9]. On the other hand, in [10,11] the authors considered some operators preserving 1 ( ) = .…”