## Journal of Applied Mathematics

### Some Identities between the Extended $q$-Bernstein Polynomials with Weight $\alpha$ and $q$-Bernoulli Polynomials with Weight ($\alpha$,$\beta$)

#### Abstract

Using bosonic $p$-adic $q$-integral on ${ℤ}_{p}$, we give some interesting relationships between $q$-Bernoulli numbers with weight ($\alpha$,$\beta$) and $q$-Bernstein polynomials with weight $\alpha$. Also, using $q$-Bernstein polynomials with two variables, we derive some interesting properties associated with $q$-Bernoulli numbers with weight ($\alpha$,$\beta$).

#### Article information

Source
J. Appl. Math., Volume 2013 (2013), Article ID 604364, 8 pages.

Dates
First available in Project Euclid: 14 March 2014

https://projecteuclid.org/euclid.jam/1394808236

Digital Object Identifier
doi:10.1155/2013/604364

Mathematical Reviews number (MathSciNet)
MR3138925

Zentralblatt MATH identifier
06950779

#### Citation

Lee, H. Y.; Ryoo, C. S. Some Identities between the Extended $q$ -Bernstein Polynomials with Weight $\alpha$ and $q$ -Bernoulli Polynomials with Weight ( $\alpha$ , $\beta$ ). J. Appl. Math. 2013 (2013), Article ID 604364, 8 pages. doi:10.1155/2013/604364. https://projecteuclid.org/euclid.jam/1394808236

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