Browsing by Author "Dalmanoglu, Ozge"

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Approximation By An Integral Type Apostol-Genocchi Operators
(JOURNAL OF MATHEMATICAL ANALYSIS, 2024-08-16) Dalmanoglu, Ozge
The goal of the current paper is to present an integral type FavardSzasz operators including Apostol-Genocchi poynomials. With the help of the moments, we investigate the order of convergence in terms of the first and the second order modulus of continuity and Peetres K- functional. We also examine the convergence in the weighted spaces of functions by means of weighted Korovkin type theorem.
Approximation by Chlodowsky Type Q-Jakimovski-Leviatan Operators
(2016) Dalmanoglu, Ozge; Serenbay, Sevilay Kirci; ABF-5851-2020
This paper deals with the Chlodowsky type q-Jakimovski-Leviatan operators. We first establish approximation properties and rate of convergence results for these operators. Our main purpose is to give a theorem on the rate of convergence of the rth q-derivative of the operators.
Approximation by Truncated Lupas Operators of Max-Product Kind
(2021) Mediha, Orkcu; Dalmanoglu, Ozge; Hatipoglu, Fatma Busra
The goals of the present paper are to introduce truncated Lupas type operators of max-product kind and give an estimation for the degree of approximation with respect to first modulus of continuity function. We prove that this estimate can not be improved; on the other hand, for some subclasses of functions, better degree of approximation is obtained. We also showed the piecewise convexity of the constructed operators on the interval [0, 1].
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.
Approximation Theorems for Kantorovich Type Favard-Szasz Operators Based on q-Integers
(2017) Dalmanoglu, Ozge; Serenbay, Sevilay Kirci; ABF-5851-2020
In this paper we introduce the q-analogue of Kantorovich generalization of Favard-Szasz type operators and investigate their approximation properties. We first give basic convergence results by using Korovkin's Theorem and then estimate the rate of convergence by using modulus of continuity. We also give a local approximation theorem and study weighted approximation properties of these new operators.
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.
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.
Rate of Convergence for Generalized Szasz-Mirakyan Operators in Exponential Weighted Space
(2017) Serenbay, Sevilay Kirci; Dalmanoglu, Ozge; ABF-5851-2020
In the present paper, generalized Szasz-Mirakyan operators in exponential weighted space of functions of one variable are introduced. Using a method given by Rempulska and Walczak, some theorems on the degree of approximation are investigated. Furthermore, a numerical example with an illustrative graphic is given to show comparison for the error estimates of the operators.