• Honam Mathematical Journal
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• v.33 no.2
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• pp.261-270
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• 2011

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 $\mathbb{Z}_p$.

• Journal of applied mathematics & informatics
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• v.31 no.3_4
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• pp.523-531
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• 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.

• Honam Mathematical Journal
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• v.33 no.2
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• pp.173-179
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• 2011

The main aim of this paper is to give some relationships between q-Bernstein, higher order genocchi and Euler polynomials.

• Journal of applied mathematics & informatics
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• v.35 no.1_2
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• pp.205-215
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• 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.

• Bulletin of the Korean Mathematical Society
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• v.50 no.4
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• pp.1289-1296
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• 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.

• Honam Mathematical Journal
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• v.33 no.4
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• pp.519-527
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• 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 ${\alpha}$.

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1221-1228
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• 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.

• Honam Mathematical Journal
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• v.33 no.3
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• pp.431-439
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• 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.