Browsing by Author "Duran, Uğur"
Now showing items 1-20 of 39
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Apostol type (P, Q)-Frobenius-euler polynomials and numbers
Duran, Uğur; Açıkgöz, Mehmet (University of Kragujevac, Faculty of Science, 2018)In the present paper, we introduce (p, q)-extension of Apostol type Frobenius-Euler polynomials and numbers and investigate some basic identities and properties for these polynomials and numbers, including addition theorems, ... -
Apostol type (p, q)-Frobenius-Eulerian polynomials and numbers
Khan, Waseem Ahmad; Khan, Idrees A.; Duran, Uğur; Açıkgöz, Mehmet (Springer, 2020)The main purpose of this paper is to introduce Apostol type (p, q)-Frobenius-Eulerian numbers and polynomials and investigate some of their basic identities and properties including addition theorems, difference equations, ... -
Apostol type (p, q)-Frobenius–Eulerian polynomials and numbers
Khan, Waseem Ahmad; Khan, Idrees A.; Duran, Uğur; Açıkgöz, Mehmet (Springer, 2021)The main purpose of this paper is to introduce Apostol type (p, q)-Frobenius–Eulerian numbers and polynomials and investigate some of their basic identities and properties including addition theorems, difference equations, ... -
Bell-Based Bernoulli Polynomials with Applications
Duran, Uğur; Aracı, Serkan; Açıkgöz, Mehmet (MDPI, 2021)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 ... -
The Boole Polynomials Associated with the p-adic Gamma Function
Duran, Uğur; Açıkgöz, Mehmet (Publications de l'Institut Mathématique, 2019)We set some correlations between Boole polynomials and p-adic gamma function in conjunction with p-adic Euler contant. We develop diverse formulas for p-adic gamma function by means of their Mahler expansion and fermionic ... -
Construction of the type 2 poly-Frobenius-Genocchi polynomials with their certain applications
Duran, Uğur; Açıkgöz, Mehmet; Aracı, Serkan (Springer, 2020)Kim and Kim (Russ. J. Math. Phys. 26(1):40-49, 2019) have studied the type 2 poly-Bernoulli polynomials. Inspired by their work, we consider a new class of the Frobenius-Genocchi polynomials, which is called the type 2 ... -
Diverse Properties and Approximate Roots for a Novel Kinds of the (p, q)-Cosine and (p, q)-Sine Geometric Polynomials
Sharma, Sunil Kumar; Khan, Waseem Ahmad; Ryoo, Cheon-Seoung; Duran, Uğur (MDPI, 2022)Utilizing (p, q)-numbers and (p, q)-concepts, in 2016, Duran et al. considered (p, q)-Genocchi numbers and polynomials, (p, q)-Bernoulli numbers and polynomials and (p, q)-Euler polynomials and numbers and provided ... -
Generalized Apostol Type Polynomials Based on Twin-Basic Numbers
Duran, Uğur; Açıkgöz, Mehmet; Dutta, Hemen (Rgn Publ, 2020)In this work, we consider a class of new generating function for (p, q)-analog of Apostol type polynomials of order alpha including Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials of order alpha. By making ... -
Hermite based poly-bernoulli polynomials with a q-parameter
Duran, Uğur; Açıkgöz, Mehmet; Aracı, Serkan (Jangjeon Mathematical Society, 2018)We introduce the Hermite based poly-Bernoulli polynomials with a q parameter and give some of their basic properties including not only addition property, but also derivative properties and integral representations. We ... -
The higher-order type 2 Daehee polynomials associated with p-adic integral on ℤp
Khan, Waseem Ahmad; Younis, Jihad; Duran, Uğur; Iqbal, Azhar (Routledge, 2022)In this paper, the higher-order type 2 Daehee polynomials are introduced and some of their relations and properties are derived. Then, some p-adic integral representations of not only higher-order type 2 Daehee polynomials ... -
Modified Sumudu Transform and Its Properties
Duran, Uğur (Sakarya Üniversitesi, 2021)Saif et al. (J. Math. Comput. Sci. 21 (2020) 127-135) considered modified Laplace transform and developed some of their certain properties and relations. Motivated by this work, in this paper, we define modified Sumudu ... -
Multifarious correlations for p-adic gamma function and weighted q-Daehee polynomials
Duran, Uğur; Açıkgöz, Mehmet (Maejo University, 2019)Diverse relations and identities for p-adic gamma function and p- adic Euler constant by means of weighted p-adic q-integral on pZ and Mahler expansion of the function are investigated. Then several correlations and formulas ... -
Multifarious implicit summation formulae of Hermite-based poly-Daehee polynomials
Khan, Waseem Ahmad; Nisar, Kottakkaran Sooppy; Duran, Uğur; Açıkgöz, Mehmet; Aracı, Serkan (Natural Sciences Publishing USA, 2018)In this paper, we introduce the generating function of Hermite-based poly-Daehee numbers and polynomials. By making use of this generating function, we investigate some new and interesting identities for the Hermite-based ... -
A New Approach to the Poisson Distribution: Degenerate Poisson Distribution
Duran, Uğur; Açıkgöz, Mehmet (University of Prishtina, 2020)The main purpose of this paper is to introduce and investigate degenerate Poisson distribution which is a new extension of the Poisson distribution including the degenerate exponential function. We then provide several ... -
A New Class of Higher-Order Hypergeometric Bernoulli Polynomials Associated with Lagrange-Hermite Polynomials
Muhiuddin, Ghulam; Khan, Waseem Ahmad; Duran, Uğur; Al-Kadi, Deena (MDPI, 2021)The purpose of this paper is to construct a unified generating function involving the families of the higher-order hypergeometric Bernoulli polynomials and Lagrange-Hermite polynomials. Using the generating function and ... -
A note on q-Fubini polynomials
Duran, Uğur; Aracı, Serkan; Açıkgöz, Mehmet (Jangjeon Mathematical Society, 2019)Motivated by the construction of the generating functions of c-Bernoulli polynomials and q-Euler polynomials satisfying with their important results, we define a new g-class of the Fubini polynomials. We give some new ... -
A novel kind of hermite based frobenius type Eulerian polynomials
Khan, Waseem Ahmad; Nisar, Kottakkaran Sooppy; Açıkgöz, Mehmet; Duran, Uğur (Jangjeon Research Institute for Mathematical Sciences and Physics, 2019)We introduce a new kind of extended Hermite-based Frobenius type Eulerian polynomials and then derive diverse explicit and implicit summation equations including some symmetric formulas by utilizing series manupulation ... -
On (p, q)-Sine and (p, q)-Cosine Fubini Polynomials
Khan, Waseem Ahmad; Muhiuddin, Ghulam; Duran, Uğur; Al-Kadi, Deena (MDPI, 2022)In recent years, (p, q)-special polynomials, such as (p, q)-Euler, (p, q)-Genocchi, (p, q)-Bernoulli, and (p, q)-Frobenius-Euler, have been studied and investigated by many mathematicians, as well physicists. It is important ... -
On applications for Mahler expansion associated with p-adic q-integrals
Duran, Uğur; Açıkgöz, Mehmet (World Scientific Publishing Co. Pte Ltd, 2019)In this paper, we primarily consider a generalization of the fermionic p-adic q-integral on p including the parameters ? and ? and investigate its some basic properties. By means of the foregoing integral, we introduce two ... -
On applications of blending generating functions of q-Apostol-type polynomials
Duran, Uğur; Açıkgöz, Mehmet; Aracı, Serkan (Bulgarian Academy of Sciences, 2019)Motivated by Kurt's blending generating functions of q-Apostol polynomials [16], we investigate some new identities and relations. We also aim to derive several new connections between these polynomials and generalized ...
