Browsing by Author "Orkcu, Mediha"

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    Approximation Properties of King Type -Bernstein Operators
    (2019) Dalmanoglu, Ozge; Orkcu, Mediha
    The present paper deals mainly with a King type modification of -Bernstein operators. By improving the conditions given in Mursaleen et al. (On (p, q)-analogue of Bernstein operators. Appl Math Comput 266:874-882, 2015a), we investigate the Korovkin type approximation of both -Bernstein and King type -Bernstein operators. We also prove that the error estimation of King type of the operator is better than that of the classical one whenever 0 <= x <= 1/3.
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    ON CONVERGENCE PROPERTIES OF GAMMA-STANCU OPERATORS BASED ON q-INTEGERS
    (2016) Dalmanoglu, Ozge; Orkcu, Mediha
    In this paper we introduce Stancu type generalization of Gamma operators based on the concept of q-integers. We first establish local approximation theorems for these operators. Next, we investigate the weighted approximation properties and give an estimate for the rate of convergence using classical modulus of continuity. Lastly, we obtain a Voronovskaya type theorem.
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    On the Chlodowsky variant of Jakimovski-Leviatan-Paltanea Operators
    (2021) Dalmanoglu, Ozge; Orkcu, Mediha; AIE-5068-2022
    In the present paper, our purpose is to generalize the Jakimovski-Leviatan-Paltanea operators in the sense of Chlodowsky. After introducing the new operators we first obtain the moments of these operators in order to establish the convergency properties with the help of Korovkin's theorem. After that, we give the local approximation result and the Voronovskaya type theorem. We also examine the convergence properties of the operators in the weighted space of functions. Lastly we determine the rate of convergence of the operators with the aid of the weighted modulus of continuity.