On a conjecture concerning the sum of the squared Bernstein polynomials

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• 作者：Ioan Gavrea ^{Ioan.Gavrea@math.utcluj.ro" class="auth_mail} ; Mircea Ivan ; ^{Mircea.Ivan@math.utcluj.ro" class="auth_mail}
• 关键词：Bernstein polynomials ; Mirakjan&ndash ; Favard&ndash ; Szá ; sz operators ; Meyer-Kö ; nig and Zeller operators ; King operators
• 刊名：Applied Mathematics and Computation
• 出版年：15 August 2014
• 年：2014
• 卷：241
• 期：Complete
• 页码：70-74
• 全文大小：249 K

文摘

We obtain a new representation of the sum of the squared Bernstein polynomials and use it to validate a conjecture asserting that this sum is a convex function. The result is extended to some other classical approximation operators.