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    Generalized Baskakov type operators
    (Walter De Gruyter Gmbh, 2017) Erencin, Aysegul; Olgun, Ali; Tasdelen, Fatma
    In this paper, we introduce a generalization of Baskakov operators based on a function rho. We prove a weighted Korovkin type theorem and compute the rate of convergence via weighted modulus of continuity for these operators. Also we give a Voronovskaya type asymptotic formula.
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    Kantrovich Type Generalization of Meyer-Konig and Zeller Operators via Generating Functions
    (Ovidius Univ Press, 2013) Olgun, Ali; Ince, H. Gul; Tasdelen, Fatma
    In the present paper, we study a Kantorovich type generalization of Meyer-Konig and Zeller type operators via generating functions. Using Korovkin type theorem we first give approximation properties of these operators defined on the space C [0, Lambda], 0 < Lambda < 1. Secondly, we compute the rate of convergence of these operators by means of the modulus of continuity and the elements of the modified Lipschitz class. Finally, we give an r-th order generalization of these operators in the sense of Kirov and Popova and we obtain approximation properties of them.
  • [ X ]
    Öğe
    On approximation properties of generalized Lupas type operators based on Polya distribution with Pochhammer k-symbol
    (Hacettepe Univ, Fac Sci, 2022) Gurel Yilmaz, Ovgu; Aktas, Rabia; Tasdelen, Fatma; Olgun, Ali
    The purpose of this paper is to introduce a Kantorovich variant of Lupas-Stancu operators based on Polya distribution with Pochhammer k-symbol. We obtain rates of convergence for these operators by means of the classical modulus of continuity. Also, we give a Voronovskaja type theorem for the pointwise approximation. Furthermore, we construct a bivariate generalization of these operators and we discuss some convergence properties of them. Finally, we present some figures to compare approximation properties of our new operators with those of other operators which are mentioned in this paper. We observe that the approximation of our operators to the function f is better than that of some other operators in a certain range of values of k.