Sequence Of Linear Operators Research Articles

Convergent sequences of linear operators in semiordered spaces

The definition given by P. P. Korovkin of operators of the class Sm and conditions for the convergence of these operators to the identity operator are extended to apply to regular operators from a K-space R0 with a unit, into a K-space R1 where R0 and R1 are normally contained in the union of the spaces S [a, b] and s.

On the remainder in the approximation of functions by Bernstein-type operators

Let {,5,) be a sequence of linear operators on C [0, l] into C [0, 11. Evaluation of the remainder is useful in the investigation of the approximation properties of the operators&. For the Bernstein polynomials, this remainder has been thoroughly investi- gated. First, some asymptotic formulae were given by Voronovskaya and by Bernstein (see [IO], pp. 22-23) and later, the remainder was evaluated for different classes

On the divergence of the sequence of linear operators

On the divergence of the sequence of linear operators

ON LINEAR METHODS FOR THE SUMMABILITY OF FOURIER SERIES THAT ARE SIMILAR TO THE BERNŠTEĬN-ROGOSINSKI METHOD

We consider sequences of linear operators, the construction of which recalls the well-known Bernsteĭn-Rogosinski sums and constitutes a far-reaching generalization of them. We study conditions for the convergence of sequences of such operators, using results that we first obtain on linear summability methods for Fourier-Lebesgue series and their conjugate series.