Abstract
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.
Highlights
Let I ⊆ R be an interval and C(I) the space of all continuous, real-valued functions defined on I
Let Ln : D → C(I), n ≥ 1, be a sequence of positive linear operators, where D is a linear subspace of C(I)
We investigate the transfer of a given sequence (Ln) of positive linear operators from an interval I to another interval J, and describe the Voronovskaya type formula corresponding to the new sequence (Kn)
Summary
Ana-Maria Acua, Alexandra-Ioana Madutab and Ioan Rasab aLucian Blaga University of Sibiu, Department of Mathematics and Informatics Str. Dr I. Ratiu 5-7, RO-550012 Sibiu, Romania bTechnical University of Cluj-Napoca, Faculty of Automation and Computer Science, Department of Mathematics Str. Memorandumului 28, Cluj-Napoca, Romania
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