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SYMMETRIC IDENTITIES INVOLVING WEIGHTED q-GENOCCHI POLYNOMIALS UNDER S4
U. Duran,M. Acikgoz,S. Araci 장전수학회 2015 Proceedings of the Jangjeon mathematical society Vol.18 No.4
In the paper, we obtain some new symmetric identities of weighted q-Genocchi polynomials using the fermionic p-adic q-integral on Zp.
A note on the Frobenius-Euler numbers and polynomials associated with Bernstein polynomials
S. Araci,M. Acikgoz 장전수학회 2012 Advanced Studies in Contemporary Mathematics Vol.22 No.3
The present paper deals with Bernstein polynomials and Frobenius-Euler numbers and polynomials. We apply the method of generating function and fermionic p-adic integral representation on Z_p, which are exploited to derive further classes of Bernstein polynomials and Frobenius-Euler numbers and polynomials. To be more precise we summarize our results as follows,we obtain some combinatorial relations between Frobenius-Euler numbers and polynomials. Furthermore, we derive an integral representation of Bernstein polynomials of degree n on Z_p. Also we deduce a fermionic p-adic integral rep-resentation of product Bernstein polynomials of di¤erent degrees n_1, n_2 ,... on Z_p and show that it can be written with Frobenius-Euler numbers which yields a deeper insight into the e¤ectiveness of this type of generalizations. Our applications possess a number of interesting properties which we state in this paper.
S. Araci 장전수학회 2014 Proceedings of the Jangjeon mathematical society Vol.17 No.2
Existence and multiplicity of positive solutions for boundary-value problemsof non-linear fractional differential equations
N.K. JANGID,S. JOSHI,K. JANGID,S. ARACI,S.D. PUROHIT 장전수학회 2021 Advanced Studies in Contemporary Mathematics Vol.31 No.2
In this study, we investigate the Marichev-Saigo-Maeda fractional order differentiation and integral for the function pertaining the product of Srivastava polynomials and incomplete I-functions. More- over, their special cases are also depicted in terms of the corollaries associated with Saigo, Riemann-Liouville, and Erdelyi-Kober fractional operators.
A symmetric identity on the q-Genocchi polynomials of higher-order under third dihedral group D3
E. Agyüz,M. Acikgoz,S. Araci 장전수학회 2015 Proceedings of the Jangjeon mathematical society Vol.18 No.2
In the present paper, we perform a further investigation for the q-Genocchi numbers and polynomials of higher order under third Dihedral group D3 and establish some closed formulae of the symmetric identities. We also establish some known identities for the classical Genocchi numbers and polynomials by using fermionic p-adic integral on Zp.
SOME RESULTS ON APPROXIMATION IN 2-BANACH SPACES
AÇIKGÖZ, M,KARAKU¸S, Y,ASLAN, N,ARACI, S 장전수학회 2011 Proceedings of the Jangjeon mathematical society Vol.14 No.1
In this study, we will give some new results on the best approxi-mation and best simultaneous approximation related to the de nitions we havedone in 2-Banach spaces.
Kim, Bo Yun,Shim, In-Bo,Araci, Zeynep O.,Saavedra, S. Scott,Monti, Oliver L.A.,Armstrong, Neal R.,Sahoo, Rabindra,Srivastava, Divesh N.,Pyun, Jeffrey American Chemical Society 2010 JOURNAL OF THE AMERICAN CHEMICAL SOCIETY - Vol.132 No.10
<P><B>Graphic Abstract</B> <IMG SRC='http://pubs.acs.org/appl/literatum/publisher/achs/journals/content/jacsat/2010/jacsat.2010.132.issue-10/ja908481z/production/images/medium/ja-2009-08481z_0004.gif'> <P>The preparation of cobalt oxide nanowires with gold nanoparticle (AuNP) inclusions (Au−Co<SUB>3</SUB>O<SUB>4</SUB> nanowires) via colloidal polymerization of dipolar core−shell NPs is reported. Polystyrene-coated ferromagnetic NPs composed of a dipolar metallic cobalt shell and a gold NP core (PS−AuCoNPs) were synthesized by thermolysis of octacarbonyldicobalt [Co<SUB>2</SUB>(CO)<SUB>8</SUB>] in the presence of AuNP seeds and polymeric ligands. The colloidal polymerization process of these dipolar PS−AuCoNPs comprises dipolar nanoparticle assembly and solution oxidation of preorganized NPs to form interconnected cobalt oxide nanowires via the nanoscale Kirkendall effect, with AuNP inclusions in every repeating unit of the one-dimensional mesostructure. Calcination of the polymer-coated nanowires afforded polycrystalline Au−Co<SUB>3</SUB>O<SUB>4</SUB> nanowires that were determined to be electroactive. Nanocomposite materials were characterized by transmission electron microscopy, field-emission scanning electron microscopy, X-ray diffraction, vibrating sample magnetometry, and cyclic voltammetry. We demonstrate that the optical and electrochemical properties of Au−Co<SUB>3</SUB>O<SUB>4</SUB> nanowires are significantly enhanced in comparison with hollow Co<SUB>3</SUB>O<SUB>4</SUB> nanowires prepared via colloidal polymerization.</P></P><P><A href='http://pubs.acs.org/doi/suppl/10.1021/ja908481z'>ACS Electronic Supporting Info</A></P>
Identities involving the -Genocchi polynomials and -Zeta-type function
A. Bagdasaryan,E.Sen,Y.He,S. Araci,M. Acikgoz 장전수학회 2014 Advanced Studies in Contemporary Mathematics Vol.24 No.2
The fundamental objective of this paper is to obtain some interesting properties for (h,q)-Genocchi numbers and polynomials by using the fermionic p-adic q-integral on Zp and mentioned in the paper q-Bernstein polynomials. By applying the Mellin transformation to the generating function of (h,q)-Genochhi polynomials, we define (h,q)-Zeta-type function. Moreover, we derive symmetric properties of (h,q)-Zeta funtion and from these properties we give symmetric property of (h,q)-Genocchi polynomials.