On the properties of q-Bernstein-type polynomials
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Publisher
Natural Sciences Publishing USA
Access Rights
info:eu-repo/semantics/closedAccess
Abstract
The aim of this paper is to give a new approach to modified q-Bernstein polynomials for functions depend on the several variables. We derive the recurrence formulas related to the second Stirling numbers and generalized Bernoulli polynomials. Moreover, the interpolation function of these polynomials depend on the several variables and the derivatives of these polynomials and also their generating function are given. Final part of this paper, we get new interesting identities of modified q-Bernoulli numbers and q-Euler numbers applying p-adic q-integral representation on ?p and p-adic fermionic q-invariant integral on ?p, respectively, to the inverse of q-Bernstein polynomials. © 2017 NSP Natural Sciences Publishing Cor.
Description
Keywords
Bernoulli polynomials of higher order, Bernstein polynomial of several variables, Generating function, Mellin transformation, p-adic q-integral on ?p, Shift difference operator, Stirling numbers of the second kind
Journal or Series
Applied Mathematics and Information Sciences
WoS Q Value
Scopus Q Value
Volume
11
Issue
5
Citation
Araci, S., Acikgoz, M., & Bagdasaryan, A. (September 01, 2017). On the Properties of q-Bernstein-type Polynomials. Applied Mathematics & Information Sciences, 11, 5, 1259-1268.