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dc.contributor.authorAraci, Serkan
dc.contributor.authorAcikgoz, Mehmet
dc.date.accessioned2019-11-20T13:49:12Z
dc.date.available2019-11-20T13:49:12Z
dc.date.issued2015-01-31
dc.identifier.citationAraci, S., & Açikgöz, M. (December 01, 2015). A note on the values of weighted q-Bernstein polynomials and weighted q-Genocchi numbers. Advances in Difference Equations, 2015, 1.)en_US
dc.identifier.issn1687-1847
dc.identifier.otherWOS:000348985200004
dc.identifier.urihttps://doi.org/10.1186/s13662-015-0369-y
dc.identifier.urihttps://hdl.handle.net/20.500.11782/839
dc.description.abstractThe rapid development of q-calculus has led to the discovery of new generalizations of Bernstein polynomials and Genocchi polynomials involving q-integers. The present paper deals with weighted q-Bernstein polynomials (or called q-Bernstein polynomials with weight alpha) and weighted q-Genocchi numbers (or called q-Genocchi numbers with weight alpha and beta). We apply the method of generating function and p-adic q-integral representation on Z(p), which are exploited to derive further classes of Bernstein polynomials and q-Genocchi numbers and polynomials. To be more precise, we summarize our results as follows: we obtain some combinatorial relations between q-Genocchi numbers and polynomials with weight alpha and beta. Furthermore, we derive an integral representation of weighted q-Bernstein polynomials of degree n based on Z(p). Also we deduce a fermionic p-adic q-integral representation of products of weighted q-Bernstein polynomials of different degrees n(1), n(2), ... on Z(p) and show that it can be in terms of q-Genocchi numbers with weight alpha and beta, which yields a deeper insight into the effectiveness of this type of generalizations. We derive a new generating function which possesses a number of interesting properties which we state in this paper.en_US
dc.language.isoengen_US
dc.publisherSPRINGEROPENen_US
dc.relation.isversionof10.1186/s13662-015-0369-yen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.subjectGenocchi numbers and polynomialsen_US
dc.subjectq-Genocchi numbers and polynomialsen_US
dc.subjectweighted q-Genocchi numbers and polynomialsen_US
dc.subjectBernstein polynomialsen_US
dc.subjectq-Bernstein polynomialsen_US
dc.subjectweighted q-Bernstein polynomialsen_US
dc.titleA note on the values of weighted q-Bernstein polynomials and weighted q-Genocchi numbersen_US
dc.typearticleen_US
dc.relation.journalADVANCES IN DIFFERENCE EQUATIONSen_US
dc.contributor.departmentHKÜ, İktisadi, İdari ve Sosyal Bilimler Fakültesi, İktisat Bölümüen_US
dc.relation.publicationcategoryMakale - Uluslararası Hakemli Dergi - Kurum Öğretim Elemanıen_US


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