Faruk Özger

Prof. Faruk Özger

Izmir Kâtip Çelebi University, İzmir, Turkey (Türkiye)
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Research Focus & Metrics

Academic Career Length

16Years (2011-Present)

(Calculated once Scilit publication data is synced: current year − year of first publication + 1)

Representative Publications

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16 January 2020 in Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas
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S. A. MohiuuddinS. A. Mohiuuddin
S. A. Mohiuuddin
Faruk ÖzgerFaruk Özger
Faruk Özger

2 March 2019 in Symmetry
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Hari Mohan SrivastavaHari Mohan Srivastava
Hari Mohan Srivastava
Faruk ÖzgerFaruk Özger
Faruk Özger
S. A. MohiuuddinS. A. Mohiuuddin
S. A. Mohiuuddin
We construct Stancu-type Bernstein operators based on Bézier bases with shape parameter λ ∈ [ − 1 , 1 ] and calculate their moments. The uniform convergence of the operator and global approximation result by means of Ditzian-Totik modulus of smoothness are established. Also, we establish the direct approximation theorem with the help of second order modulus of smoothness, calculate the rate of convergence via Lipschitz-type function, and discuss the Voronovskaja-type approximation theorems. Finally, in the last section, we construct the bivariate case of Stancu-type λ -Bernstein operators and study their approximation behaviors.

21 July 2020 in Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas
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Faruk ÖzgerFaruk Özger
Faruk Özger
Hari Mohan SrivastavaHari Mohan Srivastava
Hari Mohan Srivastava
S. A. MohiuuddinS. A. Mohiuuddin
S. A. Mohiuuddin

5 January 2021 in Iranian Journal of Science and Technology, Transactions A: Science
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S. A. MohiuuddinS. A. Mohiuuddin
S. A. Mohiuuddin
NANaeem Ahmad
Naeem Ahmad
Faruk ÖzgerFaruk Özger
Faruk Özger
AAAbdullah Alotaibi
Abdullah Alotaibi
BHBipan Hazarika
Bipan Hazarika

1 January 2019 in Filomat
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Faruk ÖzgerFaruk Özger
Faruk Özger
In this study, we consider statistical approximation properties of univariate and bivariate ?-Kantorovich operators. We estimate rate of weighted A-statistical convergence and prove a Voronovskajatype approximation theorem by a family of linear operators using the notion of weighted A-statistical convergence. We give some estimates for differences of ?-Bernstein and ?-Durrmeyer, and ?-Bernstein and ?-Kantorovich operators. We establish a Voronovskaja-type approximation theorem by weighted A-statistical convergence for the bivariate case.

9 August 2021 in Mathematics
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Hari Mohan SrivastavaHari Mohan Srivastava
Hari Mohan Srivastava
KAKhursheed J. Ansari
Khursheed J. Ansari
Faruk ÖzgerFaruk Özger
Faruk Özger
Zeynep Ödemiş ÖzgerZeynep Ödemiş Özger
Zeynep Ödemiş Özger
In this study, we present a link between approximation theory and summability methods by constructing bivariate Bernstein-Kantorovich type operators on an extended domain with reparametrized knots. We use a statistical convergence type and power series method to obtain certain Korovkin type theorems, and we study certain rates of convergences related to these summability methods. Furthermore, we numerically analyze the theoretical results and provide some computer graphics to emphasize the importance of this study.