Browsing by Author "Araci, Serkan"
Now showing items 1-20 of 95
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An analogue of Eulerian polynomials related to L-type function
Araci, Serkan; Acikgoz, Mehmet; Corcino, Roberto B.; Ozel, Cenap (MAEJO UNIV, 2015-05)We introduce Dirichlet's type of twisted Eulerian polynomials by using p-adic fermionic q-invairant integral in the p-adic integer ring and obtain some new interesting identities. Using a complex contour integral representation ... -
Analogues of Newton-Girard power-sum 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, 2015-02)The Newton power-sum 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, 2018-09-01)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 Durrmeyer-Bezier type operators
Araci, Serkan; Agrawal, Purshottam N.; Bohner, Martin; Lipi, Kumari (SPRINGER INTERNATIONAL PUBLISHING A, 2018-02-22)Recently, a mixed hybrid operator, generalizing the well-known Phillips operators and Baskakov-Szasz type operators, was introduced. In this paper, we study Bezier variant of these new operators. We investigate the degree ... -
Asymptotic properties of a new Sturm-Liouville problem with retarded argument
Araci, Serkan; Acikgoz, Mehmet; Sen, Erdogan (WILEY-BLACKWELL, 2014-11-30)In this work, we study the asymptotic properties of a new Sturm-Liouville problem with retarded argument. Contrary to previous works, differential equation includes eigenparameter as a quadratic function. In the considered ... -
Blending type approximation by Stancu-Kantorovich operators based on Polya-Eggenberger distribution
Araci, Serkan; Kajla, Arun (DE GRUYTER OPEN LTD, 2017)In the paper the authors introduce the Kantorovich variant of Stancu operators based on Polya-Eggenberger distribution. By making use of this new operator, we obtain some indispensable auxiliary results. We also deal with ... -
A certain (p, q)-derivative operator and associated divided differences
Araci, Serkan; Duran, Ugur; Acikgoz, Mehmet; Srivastava, H. M. (SPRINGEROPEN, 2016)Recently, Sofonea (Gen. Math. 16:47-54, 2008) considered some relations in the context of quantum calculus associated with the q-derivative operator D-q and divided difference. As applications of the post-quantum calculus ... -
Certain fractional calculus formulas involving extended generalized Mathieu series
Araci, Serkan; Singh, Gurmej; Agarwal, Praveen; Acikgoz, Mehmet (SPRINGEROPEN, 2018-04-23)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 ... -
Certain results for the 3-variable laguerre-hermite polynomials
Nahid, Tabinda; Araci, Serkan (Natural Sciences Publishing, 1 Septembe)This paper addresses the mathematical inspection of differential and integral equations for hybrid forms of special polynomials using generating functions. The study aims to find out the differential equations of 3-variable ... -
Certain Results for the Twice-Iterated 2D q-Appell Polynomials
Araci, Serkan; Srivastava, H. M.; Yasmin, Ghazala; Muhyi, Abdulghani (MDPI, 2019-10)In this paper, the class of the twice-iterated 2D q-Appell polynomials is introduced. The generating function, series definition and some relations including the recurrence relations and partial q-difference equations of ... -
Certain Results of q-Sheffer-Appell Polynomials
Araci, Serkan; Muhyi, Abdulghani; Yasmin, Ghazala (MDPI, 2019-02)In this paper, the class of q-Sheffer-Appell polynomials is introduced. The generating function, series definition, determinant definition and some other identities of this class are established. Certain members of ... -
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 ... -
Common fixed point theorems for generalized G − η − χ− contractive type mappings with applications
Kumar, Manoj Vijaya; Araci, Serkan (Boletim da Sociedade Paranaense de Matematica, 2019)Samet et. al. (Nonlinear Anal. 75, 2012, 2154-2165) introduced the concept of α − ψ− contractive type mappings in metric spaces. In 2013, Alghamdi et. al.[2] introduced the concept of G−β−ψ−contractive type mappings in ... -
Computation of certain integral formulas involving generalized Wright function
Khan, Nabiullah; Usman, Talha; Aman, Mohd; Al-Omari, S.; Araci, Serkan (Springer, 1 December)The aim of the paper is to derive certain formulas involving integral transforms and a family of generalized Wright functions, expressed in terms of the generalized Wright hypergeometric function and in terms of the ... -
Computation of Nevanlinna characteristic functions derived from generating functions of some special numbers
Araci, Serkan; Acikgoz, Mehmet (SPRINGER INTERNATIONAL PUBLISHING AG, 2018-06)In the present paper, firstly we find a number of poles of generating functions of Bernoulli numbers and associated Euler numbers, denoted by n(a, B) and n(a, E), respectively. Secondly, we derive the mean value of a ... -
Construction of Fourier expansion of Apostol Frobenius-Euler polynomials and its applications
Araci, Serkan; Acikgoz, Mehmet (SPRINGEROPEN, 2018-02-22)In the present paper, we find the Fourier expansion of the Apostol Frobenius-Euler polynomials. By using a Fourier expansion of the Apostol Frobenius-Euler polynomials, we derive some new and interesting results. -
Construction of partially degenerate laguerre-genocchi polynomials with their applications
Usman, Talha; Aman, Mohd; Khan, Owais; Nisar, Kottakkaran Sooppy; Araci, Serkan (American Institute of Mathematical Sciences, 2020)Various applications of degenerate polynomials in different areas call for the thoughtful study and research, and many extensions and variants can be found in the literature. In this paper, we introduce partially degenerate ... -
Construction of the type 2 poly-Frobenius–Genocchi polynomials with their certain applications
Duran, Ugur; Acikgoz, Mehmet; Araci, Serkan (Springer, 1 December)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 ... -
Dunkl analogue of Szasz-Mirakjan operators of blending type
Araci, Serkan; Deshwal, Sheetal; Agrawal, P. N. (DE GRUYTER POLAND SP ZOO, 2018-11-15)In the present work, we construct a Dunkl generalization of the modified Szasz-Mirakjan operators of integral form defined by Paltanea [1]. We study the approximation properties of these operators including weighted Korovkin ... -
Estimates of certain paraxial diffraction integral operator and its generalized properties
Al-Omari, S.; Araci, Serkan; Al-Smadi, Mohammed; Gumah, Ghaleb N.; Alrabaiah, Hussam (Springer, 1 December)This paper aims to discuss a generalization of certain paraxial diffraction integral operator in a class of generalized functions. At the start of this paper, we propose a convolution formula and establish certain convolution ...
