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Kantorovich-type generalization of parametric Baskakov operators
(Wiley, 2019) Ilarslan, Hatice Gul Ince; Erbay, Hasan; Aral, Ali
In this manuscript, we define a Kantorovich generalization of the nonnegative parametric Baskakov operators. After that, the weighted uniform convergence of the generalized operators is proved. Also, we present Voronovskaja-type asymptotic approximation theorem then establish weighted approximation properties for parametric Kantorovich operator. Numerical results show that depending on the value of the parameter, we obtain a better approximation.
On discrete Picard operators
(Wiley-Blackwell, 2016) Aral, Ali; Ilarslan, Hatice Gul Ince; Tunca, Gulen Bascanbaz
The present paper is concerned with the approximation properties of discrete version of Picard operators. We first give exact equalities for the moments of the operators. In calculations of these moments, Eulerian numbers play a crucial role. We discuss convergence of these operators in weighted spaces and give Voronovskaya-type asymptotic formula. The weighted approximation of the operators in quantitative mean in terms of different modulus of continuities is also considered. We emphasize that the rate of convergence of the operators is better than the one obtained in . Copyright (c) 2016 John Wiley & Sons, Ltd.