A NOTE ON THE WEIGHTED q-BERNOULLI NUMBERS AND THE WEIGHTED q-BERNSTEIN POLYNOMIALS

• Journal title : Honam Mathematical Journal
• Volume 33, Issue 4,  2011, pp.519-527
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2011.33.4.519
Title & Authors
A NOTE ON THE WEIGHTED q-BERNOULLI NUMBERS AND THE WEIGHTED q-BERNSTEIN POLYNOMIALS
Dolgy, D.V.; Kim, T.;

Abstract
Recently, the modified q-Bernoulli numbers and polynomials with weight $\small{{\alpha}}$ are introduced in [3]: In this paper we give some interesting p-adic integral representation on $\small{\mathbb{Z}_p}$ of the weighted q-Bernstein polynomials related to the modified q-Bernoulli numbers and polynomials with weight $\small{{\alpha}}$. From those integral representation on $\small{\mathbb{Z}_p}$ of the weighted q-Bernstein polynomials, we can derive some identities on the modified q-Bernoulli numbers and polynomials with weight $\small{{\alpha}}$.
Keywords
higher order q-Bernoulli numbers and polynomials with weight $\small{{\alpha}}$;p-adic q-integral;
Language
English
Cited by
1.
On the families of q-Euler polynomials and their applications, Journal of the Egyptian Mathematical Society, 2015, 23, 1, 1
References
1.
S. Araci, D. Erdal, J. J. Seo, A study on the fermionic p-adic q-integral on Zp associated with weighted q-Bernstein and q-Genocchi polynomials, Abstract and Applied Analysis 2011(2011), Article in Press http:www.hindawi.com./26592680.

2.
T. Kim, A. Bayad, Y.-H. Kim, A study on the p-adic q-integral on ${\mathbb{Z}_P}$ associated with the weighted q-Bernstein and q-Bernoulli polynomials, J. Ineq. Appl. 2011(2011), Article ID 29513821, 8 pages.

3.
D. V. Dolgy, T. Kim, S. H. Lee, B. Lee, S. H. Rim, A note on the modified q-Bernoulli numbers and polynomials with weight $\alpha$(communicated).

4.
T. Kim, q-Volkenborn integration, Russ. J. Math. Phys. 9 (2002), 288-299.

5.
T. Kim, A note on q-Bernstein polynomials, Russ. J. Math. Phys. 18 (2011), 73-82.

6.
T. Kim, B. Lee, J. Choi, Y. H. Kim, Y. H. Kim, S, H. Rim, On the q-Euler numbers and weighted q-Bernstein polynomials, Adv. Stud. Contemp. Math. 21 (2011), 13-18.

7.
L. C. Jang, A family of Barnes-type multiple twisted q-Euler numbers and poly- nomials related to Fermionic p-adic invariant integrals on ${\mathbb{Z}_P}$, J. Comput. Anal. Appl. 13 (2011), 376-387.

8.
Y. Simsek, Special functions related to Dedekind-type DC-sums and their appli- cations, Russ. J. Math. Phys. 17 (2010), 495-508.

9.
S. H. Rim, E.-J. Moon, S.-J. Lee, J.-H. Jin, On the q-Genocchi numbers and poly-nomials associated with q-zeta function, Proc. Jangjeon Math. Soc. 12 (2009), 261-267 .

10.
T. Kim, S.-H. Lee, D. V. Dolgy, C. S. Ryoo A note on the generalized q-Bernoulli measures with weight $\alpha$, Abstract and Applied Analysis. 2011 (2011), Article ID 867217, 9 pages.