Open AccessOn the composition and decomposition of positive linear operators (VII)
Author(s) -
Ana Maria Acu,
Ioan Raşa
Publication year - 2021
Publication title -
applicable analysis and discrete mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.69
H-Index - 26
eISSN - 2406-100X
pISSN - 1452-8630
DOI - 10.2298/aadm191103006a
Subject(s) - mathematics , iterated function , operator (biology) , eigenvalues and eigenvectors , conjecture , linear map , pure mathematics , type (biology) , piecewise linear function , composition (language) , combinatorics , discrete mathematics , mathematical analysis , ecology , biochemistry , chemistry , physics , linguistics , philosophy , repressor , quantum mechanics , biology , transcription factor , gene
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 operators An and Gn. If true, this conjecture would emphasize a new and strong relationship between Gn and the classical Bernstein operator Bn.