Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
권호 표지
DOI QR코드

DOI QR Code

SOME NEW PROPERTIES ON THE q-GENOCCHI NUMBERS AND POLYNOMIALS ASSOCIATED WITH q-BERNSTEIN POLYNOMIALS

  • Araci, Serkan (Department of Mathematics, University of Gaziantep, Faculty of Science and Arts) ;
  • Erdal, Dilek (Department of Mathematics, University of Gaziantep, Faculty of Science and Arts) ;
  • Kang, Dong-Jin (Information Technology Service, Kyungpook National University)
  • Received : 2011.04.26
  • Accepted : 2011.05.10
  • Published : 2011.06.25
Download PDF
⟨ Previous Next ⟩

Abstract

The purpose of this study is to obtain some relations between q-Genocchi numbers and q-Bernstein polynomials by using fermionic p-adic q-integral on $\mathbb{Z}_p$.

Keywords

References

  1. Acikgoz, M. and Simsek, Y., A New generating function of q-Bernstein type polynomials and their interpolation function, Abstract and Applied Analysis, Article ID 769095, 12 pages, doi: 10.1155/2010/769095.01-313.
  2. Acikgoz, M., Araci, S. and Cangul, N. I., A Note on the modified q-Bernstein polynomials for functions of several variables and their reflections on q-Volkenborn integration, Applied Mathematics and Computation(in press)
  3. Gouvea, F. Q., p-adic Numbers An Introduction, 2nd Edi., Springer-Verlag, Berlin, Heidelberg and New York, 2000.
  4. Kim, T., A New Approach to q-Zeta Function, Adv. Stud. Contemp. Math. 11(2) 157-162.
  5. Kim, T., On the q-extension of Euler and Genocchi numbers, J. Math. Anal. Appl. 326 (2007) 1458-1465. https://doi.org/10.1016/j.jmaa.2006.03.037
  6. Kim, T., On the multiple q-Genocchi and Euler numbers, Russian J. Math. Phys. 15 (4) (2008) 481-486. arXiv:0801.0978v1 [math.NT] https://doi.org/10.1134/S1061920808040055
  7. Kim, T., A Note on the q-Genocchi Numbers and Polynomials, Journal of Inequalities and Applications 2007 (2007) doi:10.1155/2007/71452. Article ID 71452, 8 pages.
  8. Kim, T., A note q-Bernstein polynomials, Russ. J. Math. phys. 18(2011) , 41-50.
  9. Kim, T., q-Volkenborn integration, Russ. J. Math. phys. 9(2002) , 288-299.
  10. Kim, T., q-Bernoulli numbers and polynomials associated with Gaussian binomial coefficients, Russ. J. Math. Phys. 15(2008) , 51-57. https://doi.org/10.1134/S1061920808010068
  11. Kim, T. Choi, J. Kim, Y. H. Ryoo, C. S., On the fermionic p-adic integral representation of Bernstein polynomials associated with Euler numbers and polynomials, J. Inequal. Appl. 2010(2010), Art ID 864247, 12pp.
  12. Kim, T. Choi, J. Kim, Y. H., Some identities on the q-Bernstein polynomials, q-Stirling numbers and q-Bernoulli numbers, Adv. Stud. Contemp. Math. 20(2010) , 335-341.
  13. Kim, T., An invariant p-adic q-integrals on $Z_p$, Applied Mathematics Letters, vol. 21, pp. 105-108, 2008. https://doi.org/10.1016/j.aml.2006.11.011
  14. Kim, T. Choi, J. Kim, Y. H., q-Bernstein Polynomials Associated with q-Stirling Numbers and Carlitz's q-Bernoulli Numbers, Abstract and Applied Analysis, Article ID 150975, 11 pages, doi:10.1155/2010/150975
  15. Kim, T., A Note on the q-Genocchi Numbers and Polynomials, Journal of Inequalities and Applications, Article ID 71452, 8 pages, doi:10.1155/2007/71452.
  16. Kim, T. Choi, J. Kim, Y. H. and Jang, L. C., On p-Adic Analogue of q-Bernstein Polynomials and Related Integrals, Discrete Dynamics in Nature and Society, Article ID 179430, 9 pages, doi:10.1155/2010/179430.
  17. Kim, T., q-Euler numbers and polynomials associated with p-adic q-integrals, J. Nonlinear Math. Phys., 14 (2007), no. 1, 15-27. https://doi.org/10.2991/jnmp.2007.14.1.3
  18. Kim, T., New approach to q-Euler polynomials of higher order, Russ. J. Math. Phys., 17 (2010), no. 2, 218-225. https://doi.org/10.1134/S1061920810020068
  19. Kim, T., Some identities on the q-Euler polynomials of higher order and q-Stirling numbers by the fermionic p-adic integral on $Z_p$ , Russ. J. Math. Phys., 16 (2009), no.4, 484-491. https://doi.org/10.1134/S1061920809040037
  20. Kim, T., q-Bernoulli numbers and polynomials associated with Gaussian binomial coefficients, Russ. J. Math. Phys., 15 (2008), no. 1, 51-57. https://doi.org/10.1134/S1061920808010068
  21. Rim, S-H. Jin, J-H. Moon, E-J. and Lee, Sun-Jung., On Multiple Interpolation Functions of the q-Genocchi Polynomials, Journal of Inequalities and Applications, Article ID 13 pages, doi:10.1155/2010/351419
  22. Simsek, Y., Twisted (h, q)-Bernoulli numbers and polynomials related to twisted (h, q)-zeta function and L-function, Journal of Mathematical Analysis and Application, vol. 324, no. 2, pp. 790-804, 2006. https://doi.org/10.1016/j.jmaa.2005.12.057
  23. Jang, L-C. Ryoo, C-S., A note on the Multiple Twisted Carlitz's Type q-Bernoulli Polynomials, Abstract and Applied Analysis, Article ID 498173, 7 pages, doi:10.1155/2008/498173.

Cited by

  1. A Study on the Fermionic -Adic -Integral Representation on Associated with Weighted -Bernstein and -Genocchi Polynomials vol.2011, 2011, https://doi.org/10.1155/2011/649248
  2. Some Properties and Identities of Bernoulli and Euler Polynomials Associated withp-adic Integral onℤp vol.2012, 2012, https://doi.org/10.1155/2012/847901
  3. A NOTE ON THE WEIGHTED q-GENOCCHI NUMBERS AND POLYNOMIALS WITH THEIR INTERPOLATION FUNCTION vol.34, pp.1, 2012, https://doi.org/10.5831/HMJ.2012.34.1.11
  4. On the Values of the Weighted -Zeta and -Functions vol.2011, 2011, https://doi.org/10.1155/2011/476381