Browsing by Author "Araci, Serkan"
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A certain (p, q)derivative operator and associated divided differences
Araci, Serkan; Duran, Ugur; Acikgoz, Mehmet; Srivastava, H. M. (SPRINGEROPEN, 20161123)Recently, Sofonea (Gen. Math. 16:4754, 2008) considered some relations in the context of quantum calculus associated with the qderivative operator Dq and divided difference. As applications of the postquantum calculus ... 
A Class of Generating Functions for a New Generalization of Eulerian Polynomials with their Interpolation Functions
Araci, Serkan; Sen, Erdogan; Acikgoz, Mehmet (UNIV NIS, 2016)Motivated by a number of recent investigations, we define and investigate the various properties of a new family of the Eulerian polynomials. We derive useful results involving these Eulerian polynomials including (for ... 
A General Class of the ThreeVariable Unified ApostolType qPolynomials and Multiple Power qSums
Srivastava, Hari M.; Khan, Subuhi; Araci, Serkan; Acikgoz, Mehmet; Riyasat, Mumtaz (Springer International Publishing, 2019)The main purpose of this article is to introduce a general class of the threevariable unified Apostoltype qpolynomials and to investigate their properties and characteristics. In particular, the generating function, ... 
A Kantorovich variant of a generalized Bernstein operators
Araci, Serkan; Kajla, Arun; Agarwal, Praveen (JOURNAL MATHEMATICS & COMPUTER SCIENCEJMCS, 2019)In this note we present a Kantorovich variant of the operators proposed by [X. Y. Chen, J. Q. Tan, Z. Liu, J. Xie, J. Math. Anal. Appl., 450 (2017), 244261] based on nonnegative parameters. Here, we prove an approximation ... 
A new approach to Legendretruncatedexponentialbased Sheffer sequences via Riordan arrays
Srivastava, H. M.; Riyasat, Mumtaz; Khan, Subuhi; Araci, Serkan; Acikgoz, Mehmet (Elsevier Inc., 20200315)The significance of multivariable special polynomials has been identified both in mathematical and applied frameworks. The article aims to focus on a new class of 3variable Legendretruncatedexponentialbased Sheffer ... 
A New Class of HermiteApostol Type FrobeniusEuler Polynomials and Its Applications
Araci, Serkan; Riyasat, Mumtaz; Wani, Shahid Ahmad; Khan, Ubuhi (MDPI, 201811)The article is written with the objectives to introduce a multivariable hybrid class, namely the HermiteApostoltype FrobeniusEuler polynomials, and to characterize their properties via different generating function ... 
A new class of Laguerrebased Apostol type polynomials
Araci, Serkan; Khan, Waseem A.; Acikgoz, Mehmet (TAYLOR & FRANCIS AS, 2016)In this paper, we introduce a generating function for a new generalization of Laguerrebased ApostolBernoulli polynomials, ApostolEuler and ApostolGenocchi polynomials. By making use of the generating function method ... 
A new generalization of Apostol type HermiteGenocchi polynomials and its applications
Araci, Serkan; Khan, Waseem A.; Acikgoz, Mehmet; Ozel, Cenap; Kumam, Poom (SPRINGER INTERNATIONAL PUBLISHING AG, 20160624)By using the modified MilneThomson's polynomial given in Araci et al. (Appl Math Inf Sci 8(6):28032808, 2014), we introduce a new concept of the Apostol HermiteGenocchi polynomials. We also perform a further investigation ... 
A new symmetric endomorphism operator for some generalizations of certain generating functions
Araci, Serkan (BULGARIAN ACAD SCIENCE, 2018)In this article, we introduce new symmetric endomorphism operators by making use of appropriate infinite product series. The main results show that after direct calculations, the proposed operators are qualified to obtain ... 
A Note on the TruncatedExponential Based ApostolType Polynomials
Araci, Serkan; Srivastava, H. M.; Khan, Waseem A.; Acikgoz, Mehmet (MDPI, 201904)In this paper, we propose to investigate the truncatedexponentialbased Apostoltype polynomials and derive their various properties. In particular, we establish the operational correspondence between this new family of ... 
A note on the values of weighted qBernstein polynomials and weighted qGenocchi numbers
Araci, Serkan; Acikgoz, Mehmet (SPRINGEROPEN, 20150131)The rapid development of qcalculus has led to the discovery of new generalizations of Bernstein polynomials and Genocchi polynomials involving qintegers. The present paper deals with weighted qBernstein polynomials (or ... 
A novel approach for obtaining new identities for the lambda extension of q Euler polynomials arising from the qumbral calculus
Araci, Serkan; Acikgoz, Mehmet; Diagana, Toka; Srivastava, H. M. (INT SCIENTIFIC RESEARCH PUBLICATIONS, 2017)In this article, a new qgeneralization of the ApostolEuler polynomials is introduced using the usual qexponential function. We make use of such a generalization to derive several properties arising from the qumbral ... 
A study on a class of qEuler polynomials under the symmetric group of degree n
Araci, Serkan; Duran, Ugur; Acikgoz, Mehmet (INT SCIENTIFIC RESEARCH PUBLICATIONS, 2016)Motivated by the paper of Kim et al. [T. Kim, D. S. Kim, H. I. Kwon, J. J. Seo, D. V. Dolgy, J. Nonlinear Sci. Appl., 9 (2016), 10771082], we study a class of qEuler polynomials earlier given by Kim et al. in [T. Kim, ... 
An analogue of Eulerian polynomials related to Ltype function
Araci, Serkan; Acikgoz, Mehmet; Corcino, Roberto B.; Ozel, Cenap (MAEJO UNIV, 201505)We introduce Dirichlet's type of twisted Eulerian polynomials by using padic fermionic qinvairant integral in the padic integer ring and obtain some new interesting identities. Using a complex contour integral representation ... 
Analogues of NewtonGirard powersum formulas for entire and meromorphic functions with applications to the Riemann zeta function
Araci, Serkan; Bagdasaryan, Armen; Acikgoz, Mehmet; Srivastava, H. M. (ACADEMIC PRESS INC ELSEVIER SCIENCE, 201502)The Newton powersum formulas relate to sums of powers of roots of a polynomial with the coefficients of the polynomial. In this paper we obtain formulas that relate to sums of reciprocal powers of zeros and poles of entire ... 
Applications of fourier series and zeta functions to Genocchi polynomials
Araci, Serkan; Acikgoz, Mehmet (Natural Sciences Publishing, 20180901)In this paper, we firstly consider the properties of Genocchi polynomials, Fourier series and Zeta functions. In the special cases, we see that the Fourier series yield Zeta functions. From here, we show that zeta functions ... 
Approximation degree of DurrmeyerBezier type operators
Araci, Serkan; Agrawal, Purshottam N.; Bohner, Martin; Lipi, Kumari (SPRINGER INTERNATIONAL PUBLISHING A, 20180222)Recently, a mixed hybrid operator, generalizing the wellknown Phillips operators and BaskakovSzasz type operators, was introduced. In this paper, we study Bezier variant of these new operators. We investigate the degree ... 
Asymptotic properties of a new SturmLiouville problem with retarded argument
Araci, Serkan; Acikgoz, Mehmet; Sen, Erdogan (WILEYBLACKWELL, 20141130)In this work, we study the asymptotic properties of a new SturmLiouville problem with retarded argument. Contrary to previous works, differential equation includes eigenparameter as a quadratic function. In the considered ... 
Blending type approximation by StancuKantorovich operators based on PolyaEggenberger distribution
Araci, Serkan; Kajla, Arun (DE GRUYTER OPEN LTD, 2017)In the paper the authors introduce the Kantorovich variant of Stancu operators based on PolyaEggenberger distribution. By making use of this new operator, we obtain some indispensable auxiliary results. We also deal with ... 
Certain fractional calculus formulas involving extended generalized Mathieu series
Araci, Serkan; Singh, Gurmej; Agarwal, Praveen; Acikgoz, Mehmet (SPRINGEROPEN, 20180423)We establish fractional integral and derivative formulas by using fractional calculus operators involving the extended generalized Mathieu series. Next, we develop their composition formulas by applying the integral ...