Prof. Ugur Duran
Basic Sciences of Engineering, İskenderun Technical University, İskenderun, Hatay, Turkey (Türkiye)
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Academic Career Length
11Years (2016-Present)
(Calculated once Scilit publication data is synced: current year − year of first publication + 1)
Representative Publications
View All Publications23 November 2016 in Journal of Inequalities and Applications
Journal Article
Serkan AraciUgur DuranMAMehmet Acikgoz
Mehmet AcikgozHSHari M Srivastava
Hari M Srivastava
Recently, Sofonea (Gen. Math. 16:47-54, 2008) considered some relations in the context of quantum calculus associated with the q-derivative operator D q $D_{q}$ and divided difference. As applications of the post-quantum calculus known as the ( p , q ) $(p,q)$ -calculus, we derive several relations involving the ( p , q ) $(p,q)$ -derivative operator and divided differences.
Journal Article
In this paper, we consider Bell-based Stirling polynomials of the second kind and derive some useful relations and properties including some summation formulas related to the Bell polynomials and Stirling numbers of the second kind. Then, we introduce Bell-based Bernoulli polynomials of order and investigate multifarious correlations and formulas including some summation formulas and derivative properties. Also, we acquire diverse implicit summation formulas and symmetric identities for Bell-based Bernoulli polynomials of order . Moreover, we attain several interesting formulas of Bell-based Bernoulli polynomials of order arising from umbral calculus.
1 January 2018 in Applied Mathematics & Information Sciences
Journal Article
Journal Article
Kim and Kim (Russ. J. Math. Phys. 26, 2019, 40-49) introduced polyexponential function as an inverse to the polylogarithm function and by this, constructed a new type poly-Bernoulli polynomials. Recently, by using the polyexponential function, a number of generalizations of some polynomials and numbers have been presented and investigated. Motivated by these researches, in this paper, multi-poly-Euler polynomials are considered utilizing the degenerate multiple polyexponential functions and then, their properties and relations are investigated and studied. That the type 2 degenerate multi-poly-Euler polynomials equal a linear combination of the degenerate Euler polynomials of higher order and the degenerate Stirling numbers of the first kind is proved. Moreover, an addition formula and a derivative formula are derived. Furthermore, in a special case, a correlation between the type 2 degenerate multi-poly-Euler polynomials and degenerate Whitney numbers is shown.
1 November 2016 in Journal of Computational and Theoretical Nanoscience
Journal Article
In the present paper, we introduce a new kind of Bernoulli, Euler and Genocchi polynomials based on the (p,q)-calculus and investigate their some properties involving addition theorems, difference equations, derivative properties, recurrence relationships, and so on. We also derive (p,q)-analogues of some known formulae belong to usual Bernoulli, Euler and Genocchi polynomials. Moreover, we get (p,q)-extension of Cheon’s main result. Furthermore, we discover (p,q)-analogue of the main results given earlier by Srivastava and Pintér.
1 March 2019 in Indagationes Mathematicae
Journal Article
About Me
Dr. Uğur Duran is now an Associated Research Professor (since July 2022) at İskenderun Technical University, Türkiye, and earlier held a position as Assistant Professor Doctor (October 2020-July 2022) and as University Lecturer in the same university (February 2018- October 2020). He graduated from the Department of Mathematics in 2014 and completed an M.Sc. (in 2016), and a Ph.D. (in 2020) in Analysis and the Theory of Functions from the Gaziantep University, Gaziantep, Türkiye. He was awarded by The Graduate School of Natural and Applied Science, Gaziantep University as “The Award of Master Thesis for 2015-2016 Academic Year” thanks to his good Master's Thesis (Titled “Post Quantum Calculus”) and several quality research papers indexed by SCI-Expanded and Scopus. Also, Dr. Uğur Duran was awarded by The Scientific and Technological Research Council of Turkey (TUBITAK) for 2211-A Ph.D. Scholarship along the dates 2016-2020. Dr. Uğur Duran has more than 90 research papers in valuable international journals. He has participated in various International Conferences and presented research papers. Also, Dr. Uğur Duran has worked on analytic number theory, special polynomials, p-adic analysis, post quantum calculus ((p,q)-calculus), special functions and etc. He has served as a reviewer (more than 150 times) and as an editor in several international journals.Current Address:Department of the Basic Concepts of Engineering, İskenderun Technical University, Turkiye.
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