Profile URL: https://hdl.handle.net/20.500.13091/13578
Job Title:Doç. Dr.
Email Address:mbodur@ktun.edu.tr
Main Affiliation:02.05. Department of Engineering Basic Sciences
Status: Current Staff
ORCID:
0000-0002-9195-9043
0000-0002-9195-9043Scopus ID:
57205145132
57205145132YÖK Akademik: C7386AB38D7C63B5
Google Scholar:
VuLK19gAAAAJ
VuLK19gAAAAJWeb of Science ID:
JPK-4453-2023
JPK-4453-2023Name Variants:
Bodur, M.
6 results
Scholarly Output Search Results
Now showing 1 - 6 of 6
Article Citation - WoS: 2Citation - Scopus: 2Bivariate Bernstein Chlodovsky Operators Preserving Exponential Functions and Their Convergence Properties(Taylor & Francis Inc, 2023-12-29) Acar, Tuncer; Bodur, Murat; Isikli, Esmahis paper is devoted to an extension of the bivariate generalized Bernstein-Chlodovsky operators preserving the exponential function exp (2,2) where exp (alpha,beta)=e(-alpha x-beta y),alpha,beta is an element of R-0(+) and x,y >= 0. For these operators, we first examine the weighted approximation properties for continuous functions in the weighted space, and in the latter case, we also obtain the convergence rate for these operators using a weighted modulus of continuity. Then, we investigate the order of approximation regarding local approximation results via Peetre's K-functional. We introduce the GBS (Generalized Boolean Sum) operators of generalized Bernstein-Chlodovsky operators, and we estimate the degree of approximation in terms of the Lipschitz class of B & ouml;gel continuous functions and the mixed modulus of smoothness. Finally, we provide some numerical and graphical examples with different values to demonstrate the rate of convergence of the constructed operators.Article Weighted Approximation Results for Lupas,-Jain Operators via Summability Methods(Math. Soc. Serbia-Društvo Matematičara Srbije, 2026) Gulfirat, Mustafa; Bodur, MuratA central issue of the present paper is to consider the Korovkin-type approximation properties of the Lupa,s-Jain operators using A-statistical convergence and Abel convergence, which are well-known summability methods. We provide an instance of a sequence of positive linear operators to which the weighted Korovkin-type theorem does not apply, but the A-statistical approximation theorem does. Our results are one-way more substantial than some approximation results given in [Ba,scanbaz-Tunca et al., On Lupa,s-Jain Operators, Stud. Univ. Babe,s-Bolyai Math., 63(4) (2018), 525-537].Article Approximation by Bivariate Szasz-Mirakyan Operators Preserving E-2(p1+p2)(Univ Nis, Fac Sci Math, 2025) Bodur, MuratThe present paper is dedicated to the modification of the bivariate generalized Szasz-Mirakyan operators while preserving the exponential functions exp(2, 2) where exp(tau(1), tau(2)) = e(-tau 1p1 - tau 2p2), tau(1), tau(2) is an element of R-0(+) , and p(1), p(2) >= 0. We thoroughly investigate the weighted approximation properties and also obtain the convergence rate for these operators by utilizing a weighted modulus of continuity. Additionally, we delve into the order of approximation by investigating local approximation results through Peetre's K-functional. Furthermore, we present the GBS (Generalized Boolean Sum) operators of Szasz-Mirakyan operators and obtain the order of approximation in terms of the Lipschitz class of Bogel continuous functions and the mixed modulus of smoothness. In order to enhance our theoretical findings and effectively showcase the efficiency of our developed operators, we have included a wide range of numerical examples using various values.Article Citation - WoS: 1Citation - Scopus: 2On Kantorovich Variant of Brass-Stancu Operators(De Gruyter Poland Sp Z O O, 2024) Bodur, Murat; Bostancı, Tuğba; Başcanbaz-Tunca, Gülen; Bostancl, Tuǧba; Başcanbaz‐tunca, GülenIn this study, we deal with Kantorovich-type generalization of the Brass-Stancu operators. For the sequence of these operators, we study L- p-convergence and give some upper estimates for the L- p-norm of the approximation error via first-order averaged modulus of smoothness and the first-order K K -functional. Moreover, we show that the Kantorovich generalization of each Brass-Stancu operator satisfies variation detracting property and is bounded with respect to the norm of the space of functions of bounded variation on [ 0 , 1 ]. Finally, we present graphical and numerical examples to compare the convergence of these operators to given functions under different parameters.Article On the Stancu Type of Novel Generalization of (λ, µ)-Bernstein-Kantorovich Operators(Murat TOSUN, 2026-02-26) Bodur, MuratArticle A Bézier Variant of (λ,μ)-Bernstein Operators(Springer, 2026-01-23) Qiu, Xiu-Liang; Bodur, Murat; Cai, Qing-BoThis paper mainly introduces (lambda,mu)-Bernstein-Kantorovich-Stancu-B & eacute;zier operators that are a natural continuation of Stancu-type (lambda,mu)-Bernstein-Kantorovich operators constructed by Q.-B. Cai et al. (Enhanced approximation techniques: Stancu-type (lambda,mu)-Bernstein-Kantorovich operators, 2026, https://doi.org/10.21203/rs.3.rs-4689585/v1). For these operators, we first examine the order of approximation in regards to global approximation results using a classical approach, Lipschitz class and the second modulus of continuity. Then, a Voronovskaya-type theorem is provided, which characterizes the asymptotic behavior of these operators. Furthermore, by considering the functions whose first derivatives are of bounded variation, we give the rate of convergence of such operators. Finally, to compare the convergence of such operators both to the (lambda,mu)-Bernstein-Kantorovich-Stancu operators and to themselves for different parameters, we provide some graphical and numerical examples.
Research Topics
Domains
Physical SciencesSocial Sciences
Fields
MathematicsDecision Sciences
Subfields
Statistics and ProbabilityNumerical AnalysisApplied MathematicsManagement Science and Operations Research
Specific Research Areas
Approximation Theory and Sequence Spaces
Mathematical Approximation and Integration
Iterative Methods for Nonlinear Equations
Holomorphic and Operator Theory
Multi-Criteria Decision Making
Sustainable Development Goals
SDG data is not available
Documents
14
Citations
93
h-index
5
Documents
13
Citations
46
Publication Collaboration
| Affiliation Name | Count |
|---|---|
| Ankara University | 9 |
| Konya Technical University | 4 |
| Kırıkkale University | 2 |
| Selçuk University | 1 |
| Jimei University | 1 |
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Data obtained from OpenAlex
| Journal | Count |
|---|---|
| Demonstratio Mathematica | 1 |
| Filomat | 1 |
| Journal of Inequalities and Applications | 1 |
| Matematicki Vesnik | 1 |
| Mathematical Sciences and Applications E-Notes | 1 |
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Scholarly Output
6
Articles
6
Views / Downloads
14/0
Supervised MSc Theses
0
Supervised PhD Theses
0
WoS Citation Count
3
Scopus Citation Count
4
Patents
0
Projects
0
WoS Citations per Publication
0.50
Scopus Citations per Publication
0.67
Open Access Source
4
Supervised Theses
0
Scopus Quartile Distribution
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