Asymptotic properties of Kantorovich-type Szász–Mirakjan operators of higher order

In this paper we study local approximation properties of a higher order Kantorovich-type Szász–Mirakjan operator recently introduced by Sabancigil, Kara, and Mahmudov. We derive the complete asymptotic expansion for these operators. They generalize the Szász–Mirakjan operators of Kantorovich-type and approximate locally integrable functions satisfying a certain growth condition on the infinite interval \(0,\infty\).

Ulrich Abel
Technische Hochschule Mittelhessen, Fachbereich MND, Wilhelm-Leuschner-Strasse 13, 61169 Friedberg, Germany

Octavian Agratini
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy, Street Fântânele, nr. 57, 400320 Cluj-Napoca, Romania

Mircea Ivan
Technical University of Cluj-Napoca, Str. Memorandumului nr. 28, 400114 Cluj-Napoca, Romania

Linear positive operator; Szasz operator; Kantorovich operator; Stirling numbers.

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also freely available at the publisher: https://doi.org/10.3934/mfc.2023003

U. Abel, O. Agratini, M. Ivan, Asymptotic properties of Kantorovich-type Szász–Mirakjan operators of higher order, Mathematical Foundations of  Computing, 2023, https://doi.org/10.3934/mfc.2023003

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