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Korovkin-type approximation by operators in Riesz spaces via power series method

Chil Elmiloud, Assili Marwa

Demonstratio Mathematica

2019

Vol. 52, nr 1

490--495

In this paper we prove an Ozguç, Yurdakadim and Taş version of the Korovkin-type approximation by operators in the sense of the power series method. That is, we try to extend the Korovkin approximation theorems, obtained by Ozguç and Taş in 2016, and Taş and Yurdakadim in 2017, for concrete classes of Banach spaces to the class of Riesz spaces. Some applications are presented.

Reduction of power series in a polydisc with respect to a Gröbner basis

Szpond J.

Bulletin of the Polish Academy of Sciences. Mathematics

2005

Vol. 53, no 2

137-145

We deal with a reduction of power series convergent in a polydisc with respect to a Gröbner basis of a polynomial ideal. The results are applied to proving that a Nash function whose graph is algebraic in a “large enough” polydisc, must be a polynomial. Moreover, we give an effective method for finding this polydisc.