• Title/Summary/Keyword: q-Bernstein polynomials

Search Result 8, Processing Time 0.019 seconds

A NOTE ON THE q-EULER NUMBERS AND POLYNOMIALS WITH WEAK WEIGHT α AND q-BERNSTEIN POLYNOMIALS

  • Lee, H.Y.;Jung, N.S.;Kang, J.Y.
    • Journal of applied mathematics & informatics
    • /
    • v.31 no.3_4
    • /
    • pp.523-531
    • /
    • 2013
  • In this paper we construct a new type of $q$-Bernstein polynomials related to $q$-Euler numbers and polynomials with weak weight ${\alpha}$ ; $E^{(\alpha)}_{n,q}$, $E^{(\alpha)}_{n,q}(x)$ respectively. Some interesting results and relationships are obtained.

A RESEARCH ON A NEW APPROACH TO EULER POLYNOMIALS AND BERNSTEIN POLYNOMIALS WITH VARIABLE [x]q

  • JUNG, NAM SOON;RYOO, CHEON SEOUNG
    • Journal of applied mathematics & informatics
    • /
    • v.35 no.1_2
    • /
    • pp.205-215
    • /
    • 2017
  • In this paper, we consider a modified Euler polynomials ${\tilde{E}}_{n,q}(x)$ with variable $[x]_q$ and investigate some interesting properties of the Euler polynomials. We also give some relationships between the modified Euler polynomials and their Hurwitz zeta function. Finally, we derive some identities associated with Bernstein polynomials.

SOME IDENTITIES ON THE BERNSTEIN AND q-GENOCCHI POLYNOMIALS

  • Kim, Hyun-Mee
    • Bulletin of the Korean Mathematical Society
    • /
    • v.50 no.4
    • /
    • pp.1289-1296
    • /
    • 2013
  • Recently, T. Kim has introduced and analysed the $q$-Euler polynomials (see [3, 14, 35, 37]). By the same motivation, we will consider some interesting properties of the $q$-Genocchi polynomials. Further, we give some formulae on the Bernstein and $q$-Genocchi polynomials by using $p$-adic integral on $\mathbb{Z}_p$. From these relationships, we establish some interesting identities.

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

  • Dolgy, D.V.;Kim, T.
    • Honam Mathematical Journal
    • /
    • v.33 no.4
    • /
    • pp.519-527
    • /
    • 2011
  • Recently, the modified q-Bernoulli numbers and polynomials with weight ${\alpha}$ are introduced in [3]: In this paper we give some interesting p-adic integral representation on $\mathbb{Z}_p$ of the weighted q-Bernstein polynomials related to the modified q-Bernoulli numbers and polynomials with weight ${\alpha}$. From those integral representation on $\mathbb{Z}_p$ of the weighted q-Bernstein polynomials, we can derive some identities on the modified q-Bernoulli numbers and polynomials with weight ${\alpha}$.

SOME IDENTITIES OF THE GENOCCHI NUMBERS AND POLYNOMIALS ASSOCIATED WITH BERNSTEIN POLYNOMIALS

  • Lee, H.Y.;Jung, N.S.;Ryoo, C.S.
    • Journal of applied mathematics & informatics
    • /
    • v.29 no.5_6
    • /
    • pp.1221-1228
    • /
    • 2011
  • Recently, several mathematicians have studied some interesting relations between extended q-Euler number and Bernstein polynomials(see [3, 5, 7, 8, 10]). In this paper, we give some interesting identities on the Genocchi polynomials and Bernstein polynomials.

A NOTE ON THE GENERALIZED BERNSTEIN POLYNOMIALS

  • Bayad, A.;Kim, T.;Lee, S.H.;Dolgy, D.V.
    • Honam Mathematical Journal
    • /
    • v.33 no.3
    • /
    • pp.431-439
    • /
    • 2011
  • We prove two identities for multivariate Bernstein polynomials on simplex, which are considered on a pointwise. In this paper, we study good approximations of Bernstein polynomials for every continuous functions on simplex and the higher dimensional q-analogues of Bernstein polynomials on simplex.