Browsing by Author "Aracı, Serkan"
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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 ... 
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 ... 
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 ... 
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 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 ... 
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 ... 
On weighted qDaehee polynomials with their applications
Aracı, Serkan; Duran, Uğur; Açıkgöz, Mehmet (Elsevier, 2019)In this paper, we first consider a generalization of Kim's padic qintegral on Z(p) including parameters alpha and beta. By using this integral, we introduce the qDaehee polynomials and numbers with weight (alpha, beta). ... 
Research on Some New Results Arising from Multiple qCalculus
Duran, Uğur; Açıkgöz, Mehmet; Aracı, Serkan (University of Nis, 2018)In this paper, we develop the theory of the multiple qanalogue of the Heine's binomial formula, chain rule and Leibniz's rule. We also derive many useful definitions and results involving multiple qantiderivative and ... 
Some (p, q)analogues of Apostol type numbers and polynomials
Açıkgöz, Mehmet; Aracı, Serkan; Duran, Uğur (University of Tartu Press, 2019)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 ... 
A Study on Some New Results Arising from (p, q)Calculus
Duran, Uğur; Açıkgöz, Mehmet; Aracı, Serkan (Institute of Applied Mathematics, 2020)This paper includes some new investigations and results for post quantum calculus, denoted by (p, q)calculus. A chain rule for (p, q)derivative is given. Also, a new (p, q)analogue of the exponential function is introduced ... 
Unified (p, q)analog of Apostol Type Polynomials of Order alpha
Duran, Uğur; Açıkgöz, Mehmet; Aracı, Serkan (University of Nis, 2018)In this work, we introduce a class of a new generating function for (p, q)analog of Apostol type polynomials of order a including ApostolBernoulli, ApostolEuler and ApostolGenocchi polynomials of order alpha. By making ...