Browsing by Author "Duran, Uğur"
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Apostol type (P, Q)Frobeniuseuler 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 FrobeniusEuler polynomials and numbers and investigate some basic identities and properties for these polynomials and numbers, including addition theorems, ... 
Apostol type (p, q)FrobeniusEulerian 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)FrobeniusEulerian 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, ... 
BellBased Bernoulli Polynomials with Applications
Duran, Uğur; Aracı, Serkan; Açıkgöz, Mehmet (MDPI, 2021)In this paper, we consider Bellbased 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 padic Gamma Function
Duran, Uğur; Açıkgöz, Mehmet (Publications de l'Institut Mathématique, 2019)We set some correlations between Boole polynomials and padic gamma function in conjunction with padic Euler contant. We develop diverse formulas for padic gamma function by means of their Mahler expansion and fermionic ... 
Construction of the type 2 polyFrobeniusGenocchi polynomials with their certain applications
Duran, Uğur; Açıkgöz, Mehmet; Aracı, Serkan (Springer, 2020)Kim and Kim (Russ. J. Math. Phys. 26(1):4049, 2019) have studied the type 2 polyBernoulli polynomials. Inspired by their work, we consider a new class of the FrobeniusGenocchi 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, CheonSeoung; 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 TwinBasic 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 ApostolBernoulli, ApostolEuler and ApostolGenocchi polynomials of order alpha. By making ... 
Hermite based polybernoulli polynomials with a qparameter
Duran, Uğur; Açıkgöz, Mehmet; Aracı, Serkan (Jangjeon Mathematical Society, 2018)We introduce the Hermite based polyBernoulli 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 higherorder type 2 Daehee polynomials associated with padic integral on ℤp
Khan, Waseem Ahmad; Younis, Jihad; Duran, Uğur; Iqbal, Azhar (Routledge, 2022)In this paper, the higherorder type 2 Daehee polynomials are introduced and some of their relations and properties are derived. Then, some padic integral representations of not only higherorder type 2 Daehee polynomials ... 
Modified Sumudu Transform and Its Properties
Duran, Uğur (Sakarya Üniversitesi, 2021)Saif et al. (J. Math. Comput. Sci. 21 (2020) 127135) 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 padic gamma function and weighted qDaehee polynomials
Duran, Uğur; Açıkgöz, Mehmet (Maejo University, 2019)Diverse relations and identities for padic gamma function and p adic Euler constant by means of weighted padic qintegral on pZ and Mahler expansion of the function are investigated. Then several correlations and formulas ... 
Multifarious implicit summation formulae of Hermitebased polyDaehee 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 Hermitebased polyDaehee numbers and polynomials. By making use of this generating function, we investigate some new and interesting identities for the Hermitebased ... 
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 HigherOrder Hypergeometric Bernoulli Polynomials Associated with LagrangeHermite Polynomials
Muhiuddin, Ghulam; Khan, Waseem Ahmad; Duran, Uğur; AlKadi, Deena (MDPI, 2021)The purpose of this paper is to construct a unified generating function involving the families of the higherorder hypergeometric Bernoulli polynomials and LagrangeHermite polynomials. Using the generating function and ... 
A note on qFubini polynomials
Duran, Uğur; Aracı, Serkan; Açıkgöz, Mehmet (Jangjeon Mathematical Society, 2019)Motivated by the construction of the generating functions of cBernoulli polynomials and qEuler polynomials satisfying with their important results, we define a new gclass 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 Hermitebased 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; AlKadi, Deena (MDPI, 2022)In recent years, (p, q)special polynomials, such as (p, q)Euler, (p, q)Genocchi, (p, q)Bernoulli, and (p, q)FrobeniusEuler, have been studied and investigated by many mathematicians, as well physicists. It is important ... 
On applications for Mahler expansion associated with padic qintegrals
Duran, Uğur; Açıkgöz, Mehmet (World Scientific Publishing Co. Pte Ltd, 2019)In this paper, we primarily consider a generalization of the fermionic padic qintegral 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 qApostoltype polynomials
Duran, Uğur; Açıkgöz, Mehmet; Aracı, Serkan (Bulgarian Academy of Sciences, 2019)Motivated by Kurt's blending generating functions of qApostol polynomials [16], we investigate some new identities and relations. We also aim to derive several new connections between these polynomials and generalized ...