0000000001145605
AUTHOR
Ana Acu Maria
showing 2 related works from this author
On the composition and decomposition of positive linear operators (VII)
2021
In the present paper we study the compositions of the piecewise linear interpolation operator S?n and the Beta-type operator B?n, namely An:= S?n ?B?n and Gn := B?n ? S?n. Voronovskaya type theorems for the operators An and Gn are proved, substantially improving some corresponding known results. The rate of convergence for the iterates of the operators Gn and An is considered. Some estimates of the differences between An, Gn, Bn and S?n, respectively, are given. Also, we study the behaviour of the operators An on the subspace of C[0,1] consisting of all polygonal functions with nodes {0, 1/2,..., n-1/n,1}. Finally, we propose to the readers a conjecture concerning the eigenvalues of the ope…
On difference of operators with different basis functions
2019
In the recent years several researchers have studied problems concerning the difference of two linear positive operators, but all the available literature on this topic is for operators having same basis functions. In the present paper, we deal with the general quantitative estimate for the difference of operators having different basis functions. In the end we provide some examples. The estimates for the differences of two operators can be obtained also using classical result of Shisha and Mond. Using numerical examples we will show that for particular cases our result improves the classical one.