Posts by Octavian Agratini


We establish an asymptotic formula for a general sequence of positive linear operators of discrete type. This class represents a generalization in q-Calculus of the operators introduced by C. Mastroianni, the construciton taking its origin in a paper of Baskakov. We also mark out Voronovskaja-type formulae for two particular cases which are q-extensions of the Szasz-Mirakjan operator and the ordinary Baskakov operator.


Octavian Agratini
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania

Cristina Radu
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania


Linear positive operator, q-integers, Voronovskaja-type formula.

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O. Agratini, C. Radu, Asymptotic formulae for Baskakov-Mastroianni operators based on q-integers, Supllemento ai Rendiconti del Circolo Matematico di Palermo, Serie II 82  (2010), pag. 195-206


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Supllemento ai Rendiconti del Circolo Matematico di Palermo, Serie II

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[1] O. Agratini, C. Radu, On q-Baskakov-Mastroianni Operators, Rocky Mounatin J. Math., (accepted for publicaiton).
[2] F. Altomare,  Korovkin-type theorems and Approximation by Positive Linear Operators, Surveys in approximation Theory (SAT), 2010 (to appear).
[3] F. Altomare, M. Campiti,  Korovkin-type Approximation Theory and its Applicaitons,  de Gruyter Studies in Mathematics, vol. 17, Walter de Gruyter, Berlin, 1994.
[4] G.E. Andrews, q-Series: Their Development and Appicaiton in Analysis, Number Theory Combinatorics, Physics, and Computer Algebra, Conference Board of the Mathematical Sciences, Number 66, American Mathematical Society, 1986.
[5] A. Aral, A generalization of Szasz-Mirakjan Operators Based on q-Integers, Math. Comput. Model. 47 (2008), 1052-1062.
[6] V.A. Baskakov,  An Example of a Sequence of Linear Positive Operators in the space of Continuous Functions,  Dokl., Akad, Nauk, SSSR 113 (1957), 249-251, (in Russian).
[7] V. Kac, P. Cheung,  Quantum Calculus,  Universitext, Springer-Verlag, New York, 2002.
[8] G. Mastroianni,  Su un Operatore Lineare e Positivo,  Rend. Acc. Sc. Fis. Mat., Napoli, Serie IV, 46 (1979), 161-176.
[9] C. Radu, On Statistical Approximation of a General Class of Positive Linear Operatores Extended in q-Calculus,  Appl. Math. Comput. 215 (2009), 6, 2317-2325.

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