A Weighted Generalization of Szász-Mirakyan and Butzer Operators

Della Vecchia, Biancamaria and Mastroianni, Giuseppe and Szabados, József (2015) A Weighted Generalization of Szász-Mirakyan and Butzer Operators. Mediterranean Journal of Mathematics, 12. pp. 433-454. ISSN 1660-5446

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Abstract

Two operators are introduced for the weighted Lp approximation on the semiaxis with weight wβ(x) = xαexp(-xβ), α > -1/p, 0 < β ≤ 1, allowing a much wider class of functions than in the case of classical Szász-Mirakyan and Butzer operators. It is shown that in case 1/2 < β ≤ 1, only pointwise convergence holds, while for 0 < β ≤ 1/2, direct and converse theorems in terms of a weighted modulus of smoothness hold. Voronǒvskaya-type relations are also proved. © 2014 Springer Basel.

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