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标题：On <svg style="vertical-align:-3.294pt;width:11.0875px;" id="M1" height="14.1125" version="1.1" viewBox="0 0 11.0875 14.1125" width="11.0875" xmlns="http://www.w3.org/2000/svg" > <g transform="matrix(1.25,0,0,-1.25,0,14.1125)"> <g transform="translate(72,-60.71)"> <text transform="matrix(1,0,0,-1,-71.95,64.04)"> <tspan style="font-size: 17.93px; " x="0" y="0">𝑝</tspan> </text> </g> </g> </svg>-Adic Analogue of <svg style="vertical-align:-3.294pt;width:11.2875px;" height="14.1125" version="1.1" viewBox="0 0 11.2875 14.1125" width="11.2875" xmlns="http://www.w3.org/2000/svg" > <g transform="matrix(1.25,0,0,-1.25,0,14.1125)"> <g transform="translate(72,-60.71)"> <text transform="matrix(1,0,0,-1,-71.95,64.04)"> <tspan style="font-size: 17.93px; " x="0" y="0">𝑞</tspan> </text> </g> </g> </svg>-Bernstein Polynomials and Related Integrals
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作者：T. Kim ; J. Choi ; Y. H. Kim 等
期刊名称：Discrete Dynamics in Nature and Society
印刷版ISSN：1026-0226
电子版ISSN：1607-887X
出版年度：2010
卷号：2010
DOI：10.1155/2010/179430
出版社：Hindawi Publishing Corporation
摘要：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.