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A class of linear positive operators in weighted spaces
(Versita, 2012) Erencin, Aysegul; Ince, H. Gul; Olgun, Ali
In this paper, we introduce a class of linear positive operators based on q-integers. For these operators we give some convergence properties in weighted spaces of continuous functions and present an application to differential equation related to q-derivatives. Furthermore, we give a Stancu-type remainder.
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.