Voronovskaya type results and operators fixing two functions

• Main Authors: Ana Maria Acu, Alexandra-Ioana Măduţa, Ioan Rasa
• Format: Article
• Language: English
• Published: Vilnius Gediminas Technical University 2021-07-01
• Series: Mathematical Modelling and Analysis
• Subjects: positive linear operators; voronovskaya type theorem; extended complete chebyshev system; operators fixing two functions
• Online Access: https://journals.vgtu.lt/index.php/MMA/article/view/13228

The present paper deals with positive linear operators which fix two functions. The transfer of a given sequence (Ln) of positive linear operators to a new sequence (Kn) is investigated. A general procedure to construct sequences of positive linear operators fixing two functions which form an Extended Complete Chebyshev system is described. The Voronovskaya type formula corresponding to the new sequence which is strongly influenced by the nature of the fixed functions is obtained. In the last section our results are compared with other results existing in literature.