Özet: Bu çalışmada, q-Baskakov operatörlerinin yeni bir türü tanıtılmıştır. Merkezi momentler için formüller elde edildilmiş. Tanımlanan q-Baskakov operatörlerinin dizilerinin yaklaşım özellikleri ve yakınsama oranı, süreklilik modülü yardımıyla belirlenmiştir.

The aim of this paper is to motivate a new sequence of positive linear operators by means of Chlodovsky-type Szasz-Mirakyan-Bernstein operators and to investigate some approximation properties of these operators in the space of continuous functions defined on the right semiaxis. We also find the order of this approximation by using the modulus of continuity and give the Voronovskаya-type theorem. Метою даної статтi є обґрунтування нової послiдовностi додатних лiнiйних операторiв за допомогою операторiв Саса-Мiракяна-Бернштейна типу Хлодовського та дослiдження деяких апроксимацiйних властивостей цих операторiв у просторi неперервних функцiй, заданих на правiй пiвосi. Крiм того, встановлено порядок таких наближень за допомогою модуля неперервностi та наведено теорему типу Вороновської.

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Abstract. This paper is concerned with some sequences of the positive linear operators based on q -Calculus. The approximation properties and the rate of convergence of these sequences of q -discrete type is established by means of the modulus of continuity. Moreover we give Voronovskaya-type theorems. Finally we present some applications such as q -Bernstein operators and q -Meyer-König and Zeller operators.Mathematics subject classification (2010): 05A30, 41A25, 41A36, 47B38.