On a certain seqence of positive linear operators and tow optimization inequalities

Abstract

In this Paper the approximation of continuous functions by positive linear operators of Bernstein type is investigated. The consideered operators are constructed using a system of rational functions with prescribed matrix of real poles. A certain general problem of S Bernstein concerning a scheme of construction of a sequence of positive linear operators is discussed. The answer on the Bernstein's hypothesis is given. The optimal limiting relations for the norm of the second central moment of our sequence of operators are established.

Keywords:

• Positive Linear Operators
• Matrix or Real Poles
• S.Bernstein's Hypothesis
• Optimal Limiting Relations