, Volume 99, Issue 3, pp 203-208

Positive linear operators which preserve x 2

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Abstract

A sequence of positive linear operators which approximate each continuous function on [0,1] while preserving the functione 2 (x) =x 2 is presented. Quantitative estimates are given and are compared with estimates of approximation by Bernstein polynomials. Connections with summability are discussed.

This revised version was published online in June 2006 with corrections to the Cover Date.