On p-Adic Analogue of q-Bernstein Polynomials and Related Integrals
نویسندگان
چکیده
Recently, Kim’s work in press introduced q-Bernstein polynomials which are different Phillips’ q-Bernstein polynomials introduced in the work by Phillips, 1996; 1997 . The purpose of this paper is to study some properties of several type Kim’s q-Bernstein polynomials to express the p-adic q-integral of these polynomials on Zp associated with Carlitz’s q-Bernoulli numbers and polynomials. Finally, we also derive some relations on the p-adic q-integral of the products of several type Kim’s q-Bernstein polynomials and the powers of them on Zp.
منابع مشابه
On q-Euler Numbers Related to the Modified q-Bernstein Polynomials
and Applied Analysis 3 see 8 . For 0 ≤ k ≤ n, derivatives of the nth degree modified q-Bernstein polynomials are polynomials of degree n − 1: d dx Bk,n ( x, q ) n ( qBk−1,n−1 ( x, q ) − q1−xBk,n−1 ( x, q )) ln q q − 1 1.9 see 8 . The Bernstein polynomials can also be defined in many different ways. Thus, recently, many applications of these polynomials have been looked for by many authors. In t...
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