Abstract
In this paper, we construct sequences of Szász–Mirakyan operators which are based on a function ρ. This function not only characterizes the operators but also characterizes the Korovkin set \({\left \{ 1,\rho ,\rho ^{2} \right \}}\) in a weighted function space. We give theorems about convergence of these operators to the identity operator on weighted spaces which are constructed using the function ρ and which are subspaces of the space of continuous functions on \({\mathbb{R} ^{+}}\). We give quantitative type theorems in order to obtain the degree of weighted convergence with the help of a weighted modulus of continuity constructed using the function ρ. Further, we prove some shape-preserving properties of the operators such as the ρ-convexity and the monotonicity. Our results generalize the corresponding ones for the classical Szász operators.
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Aral, A., Inoan, D. & Raşa, I. On the Generalized Szász–Mirakyan Operators. Results. Math. 65, 441–452 (2014). https://doi.org/10.1007/s00025-013-0356-0
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DOI: https://doi.org/10.1007/s00025-013-0356-0