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Your search keyword '"Araci, Serkan"' showing total 14 results
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14 results on '"Araci, Serkan"'

2. A new family of Apostol-Genocchi polynomials associated with their certain identities.

Author

Khan, Nabiullah, Husain, Saddam, Usman, Talha, and Araci, Serkan

Subjects
POLYNOMIALS, GENERATING functions, HYPERGEOMETRIC series, IDENTITIES (Mathematics)
Abstract

In this paper, we provide a generating function for mix type Apostol-Genocchi polynomials of order η associated with Bell polynomials. We also derive certain important identities of Apostol Genocchi polynomials of order η based on Bell polynomials, such as the correlation formula, the implicit summation formula, the derivative formula, some correlation with Stirling numbers and their special instances. Moreover, we discover some symmetric identities and their related known results. [ABSTRACT FROM AUTHOR]

Published
2023
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7. On the Properties of q-Bernstein-type Polynomials

Author

Araci, Serkan, Acikgoz, Mehmet, Jolany, Hassan, Bagdasaryan, Armen, HKÜ, İktisadi, İdari ve Sosyal Bilimler Fakültesi, and HKÜ, 0- Bölüm Yok

Subjects
Numerical Analysis, Pure mathematics, Mathematics - Number Theory, Bernoulli polynomials of higher order, Applied Mathematics, Shift difference operator, Stirling numbers of the second kind, Type (model theory), Computer Science Applications, Bernstein polynomial of several variables, p-adic q-integral on ?p, Computational Theory and Mathematics, FOS: Mathematics, Mellin transformation, p-adic q-integral on Zp, Generating function, Number Theory (math.NT), 11M06, 11B68, 11S40, 11S80, 28B99, 41A50, Analysis, Generating function (physics), Mathematics
Abstract

The aim of this paper is to give a new approach to modified $q$-Bernstein polynomials for functions of several variables. By using these polynomials, the recurrence formulas and some new interesting identities related to the second Stirling numbers and generalized Bernoulli polynomials are derived. Moreover, the generating function, interpolation function of these polynomials of several variables and also the derivatives of these polynomials and their generating function are given. Finally, we get new interesting identities of modified $q$-Bernoulli numbers and $q$-Euler numbers applying $p$-adic $q$-integral representation on $\mathbb {Z}_p$ and $p$-adic fermionic $q$-invariant integral on $\mathbb {Z}_p$, respectively, to the inverse of $q$-Bernstein polynomials., Comment: 17 pages, some theorems added to new version

Published
2017

8. Some (p, q)-analogues of Apostol type numbers and polynomials.

Author

ACIKGOZ, MEHMET, ARACI, SERKAN, and DURAN, UGUR

Subjects
*EULER polynomials, *POLYNOMIALS, *BERNOULLI polynomials, *GENERATING functions, *HERMITE polynomials, *EULER characteristic
Abstract

We consider a new class of generating functions of the generalizations of Bernoulli and Euler polynomials in terms of (p, q)-integers. By making use of these generating functions, we derive (p, q)-generalizations of several old and new identities concerning Apostol-Bernoulli and Apostol-Euler polynomials. Finally, we define the (p, q)-generalization of Stirling polynomials of the second kind of order v, and provide a link between the (p, q)-generalization of Bernoulli polynomials of order v and the (p, q)-generalization of Stirling polynomials of the second kind of order v. [ABSTRACT FROM AUTHOR]

Published
2019
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9. ON (q,r,w)-STIRLING NUMBERS OF THE SECOND KIND.

Author

DURAN, UGUR, ACIKGOZ, MEHMET, and ARACI, SERKAN

Subjects
BERNOULLI polynomials, NUMERICAL analysis
Abstract

In this paper, we introduce a new generalization of the r-Stirling numbers of the second kind based on the q-numbers via an exponential generating function. We investigate their some properties and derive several relations among q-Bernoulli numbers and polynomials, and newly defined (q, r,w)- Stirling numbers of the second kind. We also obtain q-Bernstein polynomials as a linear combination of (q,r,w)-Stirling numbers of the second kind and q-Bernoulli polynomials in w. [ABSTRACT FROM AUTHOR]

Published
2018

10. Some new identities on the Apostol-Bernoulli polynomials of higher order derived from Bernoulli basis.

Author

Bagdasaryan, Armen, Araci, Serkan, Acikgoz, Mehmet, and Yuan He

Subjects
BERNOULLI polynomials, HERMITE polynomials, GENERATING functions
Abstract

In the present paper, we introduce a method in order to obtain some new interesting relations and identities of the Apostol-Bernoulli polynomials of higher order, which are derived from Bernoulli polynomial basis. Finally, by utilizing this method, we also get formulas for the convolutions of Bernoulli and Euler polynomials in terms of Apostol-Bernoulli polynomials of higher order. [ABSTRACT FROM AUTHOR]

Published
2016
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11. On the von Staudt–Clausen's theorem related to q-Frobenius–Euler numbers.

Author

Araci, Serkan and Acikgoz, Mehmet

Subjects
*FROBENIUS algebras, *ASSOCIATIVE algebras, *QUASI-Frobenius rings, *CONGRUENCE lattices, *LATTICE theory
Abstract

In this paper, we introduce q -Frobenius–Euler numbers and derive some new properties. From those properties, we show that this number is a p -adic integer, and can be expressed by von Staudt–Clausen's theorem. We also get a type of Kummer congruence for this number. [ABSTRACT FROM AUTHOR]

Published
2016
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12. ON (q, r, w)-STIRLING NUMBERS OF THE SECOND KIND

Author

Ugur Duran, Acikgoz, Mehmet, Araci, Serkan, and HKÜ, İktisadi, İdari ve Sosyal Bilimler Fakültesi, İktisat Bölümü

Subjects
q-Calculus, Stirling numbers of the second kind, Bernoulli polynomials and numbers, Generating function, Cauchy product, algebra_number_theory
Abstract

In this paper, we introduce a new generalization of the r-Stirling numbers of the second kind based on the q-numbers via an exponential generating function. We investigate their some properties and derive several relations among q-Bernoulli numbers and polynomials, and newly defined (q, r, w)Stirling numbers of the second kind. We also obtain q-Bernstein polynomials as a linear combination of (q, r, w)-Stirling numbers of the second kind and q-Bernoulli polynomials in w.

13. (P, q) -Bernoulli, (p, q) -Euler ve (p, q) -genokchi polinomları

Author

HKÜ, İktisadi, İdari ve Sosyal Bilimler Fakültesi, İktisat Bölümü, Duran, Ugur, Acikgoz, Mehmet, and Araci, Serkan

Subjects
(PQ)-calculus, Genocchi polynomials of order α, Bernoulli polynomials of order α, Euler polynomials of order α, Generating function
Abstract

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. © 2016 American Scientific Publishers All rights reserved.

Published
2016

14. On (p,q)-Bernoulli, (p,q)-Euler and (p,q)-genocchi polynomials

Author

Ugur Duran, Serkan Araci, Mehmet Acikgoz, Duran, Ugur, Acikgoz, Mehmet, and Araci, Serkan

Subjects
(PQ)-calculus, Genocchi polynomials of order α, 02 engineering and technology, 01 natural sciences, Classical orthogonal polynomials, symbols.namesake, Macdonald polynomials, Wilson polynomials, 0202 electrical engineering, electronic engineering, information engineering, General Materials Science, 0101 mathematics, Electrical and Electronic Engineering, Mathematics, Generating function, Discrete mathematics, Discrete orthogonal polynomials, 010102 general mathematics, General Chemistry, Condensed Matter Physics, Bernoulli polynomials, Computational Mathematics, Difference polynomials, Hahn polynomials, Orthogonal polynomials, symbols, 020201 artificial intelligence & image processing, Bernoulli polynomials of order α, Euler polynomials of order α
Abstract

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. © 2016 American Scientific Publishers All rights reserved.

Published
2016

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