2011•Unpublished venueRequires access

ON A GENERAL CLASS OF LINEAR AND POSITIVE OPERATORS

Ovidiu T. Pop, Mircea D. F

Abstract

Suppose that (Lm)m≥1 is a given sequence of linear and positive operators. Starting with the mentioned sequence, the new sequence (Km)m≥1 of linear and positive operators is constructed. For the operators (Km)m≥1 a convergence theorem and a Voronovskaja-type theorem are established. As particular cases of the general construction, we refined the Bernstein’s operators, the Stancu’s operators, the Mirakyan-Favard-Szasz operators, the Baskakov operators, the Bleimann-Butzer-Hahn operators, the Meyer-König-Zeller operators, the Ismail-May operators. 1

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Key concepts: Baskakov operator, Mathematics, Spectral theorem, Linear operators, Operator theory, Sequence (biology), Operator norm, Class (philosophy)