Properties of discrete non-multiplicative operators


The paper is focused on general sequences of discrete linear operators, say \((L_{n})_{n}\geq1\). The special case of positive operators is also to our attention. Concerning the quantity \(\triangle(L_{n},f,g):=L_{n}(f_{g})-(L_{n}f)(L_{n}g)\),\(\ f\) and g belonging to some certain spaces, we propose different estimates. Firstly, we study its asymptotic behavior in Voronovskaja’s sense. Examples are presented. Secondly, we prove an extension of Chebyshev-Gruss type inequality for the above quantity. Special cases are investigated separately. Finally we establish sufficient conditions that ensure statistical convergence of the sequence \(\triangle(L_{n},f,g)\).


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


Linear operator ·Voronovskaja formula · Grüss-type inequality · Bernstein operator · Jain operator · Generalized sample operator · Statistical convergence

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O. Agratini, Properties of discrete non-multiplicative operators, Analysis and Mathematical Physics, 9 (2020), pp. 131-141.


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