On 𝑝-Adic Analogue of 𝑞-Bernstein Polynomials and Related Integrals - T. Kim; J. Choi; Y. H. Kim; L. C. Jang (Discrete Dynamics in Nature and Society)
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.