TY - JOUR
AU - Stancu, Dimitrie D.
PY - 2002/02/01
Y2 - 2024/07/20
TI - Use of identity of A. Hurwitz for construction of a linear positive operator of approximation
JF - Rev. Anal. Numér. Théor. Approx.
JA - Rev. Anal. Numér. Théor. Approx.
VL - 31
IS - 1
SE - Articles
DO - 10.33993/jnaat311-714
UR - https://ictp.acad.ro/jnaat/journal/article/view/2002-vol31-no1-art13
SP - 115-118
AB - <pre>By using a general algebraic identity of Adolf Hurwitz [1], which generalizes an important identity of Abel, we construct a new operator \(S_m^{(\beta_1,\ldots,\beta_m)}\) approximating the functions. <br />A special case of this is the operator \(Q_m^\beta\) of Cheney-Sharma.</pre><pre>We show that this new operator, applied to a function \(f\in C[0,1]\), is interpolatory at both sides of the interval \([0,1]\), and reproduces the linear functions.</pre><pre>We also give an integral representation of the remainder of the approximation formula of the function \(f\) by means of this operator. By applying a criterion of T. Popoviciu [2], is also given an expression of this remainder by means of divided </pre><pre>difference of second order.</pre>
ER -