Abstract
The paper aims at approximating functions through a sequence of linear positive operators of continuous type. First we define the Appell polynomials of dimension \(d(d\geq2)\) and with their aid we expand the Sz\'{a}sz-Mirakjan operators in the Durrmeyer sense. The investigation of the new class of operators involves the study of convergence by using the universal Bohman-Korovkin theorem and the indication of the error by using modulus of smoothness. The main results are given by the asymptotic expansion of both the operators and their derivatives with the explicit specification of all coefficients in a concise form. In particular, Voronovskaja type theorems are obtained.
Authors
Ulrich Abel
Technische Hochschule Mittelhessen, Wilhelm-Leuschner-Straße 13, 61169 Friedberg, Germany
Octavian Agratini
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy, Cluj-Napoca, Romania
Radu Paltanea
Department of Mathematics, Transilvania University, Brasov, Romania
Keywords
Positive linear operator; Appell polynomial; Asymptotic expansion; Rate of convergence; Modulus of continuity.
Paper coordinates
U. Abel, O. Agratini, R. Păltănea, Szász–Mirakjan–Durrmeyer operators defined by multiple Appell polynomials, Positivity, 29 (2025), art. no. 17, https://doi.org/10.1007/s11117-024-01108-6
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1385-1292
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