On the Properties of q-Bernstein-type Polynomials

Authors

Serkan Araci, Department of Economics, Faculty of Economics, Administrative and Social Sciences, Hasan Kalyoncu University, 27410 Gaziantep, Turkey.Follow
Mehmet Acikgoz, Department of Mathematics, Faculty of Science and Arts, University of Gaziantep, 27310 Gaziantep, Turkey.Follow
Armen Bagdasaryan, Department of Mathematics and Statistics, American University of the Middle East (in affiliation with Purdue University - USA.), Kuwait.Follow

Author Country (or Countries)

Turkey.

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 Zp and p-adic fermionic q-invariant integral on Zp, respectively, to the inverse of q-Bernstein polynomials.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/amis/110503

Recommended Citation

Araci, Serkan; Acikgoz, Mehmet; and Bagdasaryan, Armen (2017) "On the Properties of q-Bernstein-type Polynomials," Applied Mathematics & Information Sciences: Vol. 11: Iss. 5, Article 3.
DOI: http://dx.doi.org/10.18576/amis/110503
Available at: https://digitalcommons.aaru.edu.jo/amis/vol11/iss5/3