Approximation by certain linear operators preserving x^2

Authors: LUCYNA REMPULSKA, KAROLINA TOMCZAK

Abstract: We investigate certain positive linear operators L_n preserving the functions e_k (x)=x^k, k=0, 1, and modified operators L_n^* which preserve e_0 and e_2. We show that the error of approximation of f by L_n^* (f) is smaller than for L_n(f).

Keywords: Positive linear operator, polynomial weighted space, degree of approximation.

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