Approximation operators – solutions and questions


The paper gartes some results concerning linear approximation operators  and it raises three open problems.


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


linear positive operator; Korovkin type theorem; convex function of n-order; divided difference

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O. Agratini, Approximation operators – solutions and questions, Seminaire de la Theorie de La Meilleure Approximation, Convexite et optimisation, 2002, pp.21-29.


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[1] M. Abramowitz, I.A. Stegun, eds., Handbook of Mathematical Funcitons with Fromulas, Graphs and Mathematical Tables,  National Bureau of Standards Applied Mathematics Series, 55, 1964.
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[3] M. Campiti, G. Metafune, Approximation Properties of Recursively Defined Bernstein-Type Operators,  J. Approx. Theory, 87 (1996), 243-269.
[4] M.K. Khan, On the Rate of Convergence of Bernstein Power Series for Funcitons of Bounded Variation,  J. Approx. Theory, 57 (1989), 90-103.
[5] H.G. Lehnhoff, On a modified Szasz-Mirakjan operator,  J. Approx. Theory, 42 (1984), 278-282.
[6] J. Wang, S. Zhou,  On the convergence of modified Baskakov operators,  Bull. Inst. Math. Academia Sinica, 28 (2000), 2, 117-123.


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