Use of identity of A.Hurwitz for construction of a linear positive operator of approximation

Authors

  • Dimitrie D. Stancu “Babes-Bolyai” University, Cluj-Napoca, Romania

Keywords:

Hurwitz's identity, Abel's generalization of the binomial formula, linear positive operator of approximation, the Peano theorem, divided difference

Abstract

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. A special case of this is the operator \(Q_m^\beta\) of Cheney-Sharma. 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. 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 difference of second order.

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Published

2002-02-01

How to Cite

Stancu, D. D. (2002). Use of identity of A.Hurwitz for construction of a linear positive operator of approximation. Rev. Anal. Numér. ThéOr. Approx., 31(1), 115-118. Retrieved from https://ictp.acad.ro/jnaat/journal/article/view/2002-vol31-no1-art13

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