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STUDIA MATHEMATICA - Issue no. 4 / 2010 | |||||||
Article: |
ON THE COMBINATORIAL IDENTITIES OF ABEL-HURWITZ TYPE AND THEIR USE IN CONSTRUCTIVE THEORY OF FUNCTIONS. Authors: ELENA IULIA STOICA. |
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Abstract: This paper is concerned with the problem of approximation of multivariate functions by means of the Abel-Hurwitz-Stancu type linear positive operators. Inspired by the work of D. D. Stancu [13], we continue the discussions of the approximation of trivariate functions by a class of Abel-Hurwitz-Stancu operators in the case of trivariate variables, continues on the unit cub K3 = [0, 1]3. In this paper there are three sections. In Section 1, which is the Introduction, is mentioned the generalization given by N. H. Abel [1] in 1826, for the Newton binomial formula and then the very important extension of this formula given by A. Hurwitz in 1902, in the paper [3]. Here is mentioned an interesting combinatorial significance in a cycle-free directed graphes given by D. E. Knuth [5]. Then is presented a main result given in 2002 by D. D. Stancu [13], where is used a variant of the Hurwitz identity in order to construct and investigate a new linear positive operator, which was used in the theory of approximation univariate functions. In Section 2 is discussed in detail the trivariate polynomial operator of Stancu-Hurwitz type ![]() ![]() Key words and phrases. Abel-Hurwitz-Stancu operators. |
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