A note on the modified q-Bernstein polynomials for functions of several variables and their reflections on q-Volkenborn integration

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• 作者：Mehmet  ; Aç ; ?kgö ; z^a ;   ; ^{acikgoz@gantep.edu.tr} ; Serkan  ; Arac?^a ;   ; ^{mtsrkn@hotmail.com} ; ?smail Naci  ; Cangü ; l^b ;   ; ^{cangul@uludag.edu.tr}
• 关键词：Generating function ; Bernstein polynomials of several variables ; Bernstein operator of several variables ; Shift difference operator ; Q-difference operator ; q-Stirling numbers ; q-Volkenborn integration ; Hermite polynomials ; Carlitz&rsq
• 刊名：Applied Mathematics and Computation
• 出版年：2011
• 出版时间：1 October 2011
• 年：2011
• 卷：218
• 期：3
• 页码：707-712
• 全文大小：181 K

文摘

In this paper, we consider the modified q-Bernstein polynomials for functions of several variables on q-Volkenborn integral and investigate some new interesting properties of these polynomials related to q-Stirling numbers, Hermite polynomials and Carlitz¡¯s type q-Bernoulli numbers.