A note on q-Bernstein polynomials

A Note on the Modified q-Bernstein Polynomials

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

In this paper we construct a new type of q-Bernstein polynomials related to q-Euler numbers and polynomials with weak weight α ; E (α) n,q , E (α) n,q (x) respectively. Some interesting results and relationships are obtained. AMS Mathematics Subject Classification : 11B68, 11S40, 11S80.

Some Identities on the q-Tangent Polynomials and Bernstein Polynomials

In this paper, we investigate some properties for the q-tangent numbers and polynomials. By using these properties, we give some interesting identities on the q-tangent polynomials and Bernstein polynomials. Throughout this paper, let p be a fixed odd prime number. The symbol, Zp, Qp and Cp denote the ring of p-adic integers, the field of p-adic rational numbers and the completion of algebraic ...

A Note on Generalized q-Boole Polynomials

Let p be a prime number with p ≡ 1(mod 2). Throughout this paper, Zp,Qp and Cp will denote the ring of p-adic integers, the field of p-adic rational numbers and the completion of algebraic closure of Qp. The p-adic norm | · |p is normalized as |p|p = 1 p . Let q be an indeterminate in Cp such that |1− q|p < p −1 p−1 . The q-extension of number x be defined as [x]q = 1−qx 1−q . Note that limq→1[...

Some Identities on the Twisted (h, q)-Genocchi Numbers and Polynomials Associated with q-Bernstein Polynomials

Let p be a fixed odd prime number. Throughout this paper, we always make use of the following notations: Z denotes the ring of rational integers, Zp denotes the ring of padic rational integer, Qp denotes the ring of p-adic rational numbers, and Cp denotes the completion of algebraic closure of Qp, respectively. Let N be the set of natural numbers and Z N {0}. Let Cpn {ζ | ζpn 1} be the cyclic g...