关于近似积分中的几个极值问题
On some extremalities in the approximate integration
摘要：
对高阶凸函数证明了求积算子的一些极值。这样的结果在数值分析中是已知的，然而它们通常在适当的可微性假设下被证明。在我们的考虑中，除了高阶凸性本身之外，我们不使用任何其他假设。所得不等式改进了Hadamard型不等式.在较弱的假设条件下，给出了正交算子的误差界。
英文摘要：
Some extremalities for quadrature operators are proved for convex functions of higher order. Such results are known in the numerical analysis, however they are often proved under suitable differentiability assumptions. In our considerations we do not use any other assumptions apart from higher order convexity itself. The obtained inequalities refine the inequalities of Hadamard type. They are applied to give error bounds of quadrature operators under the assumptions weaker from the commonly used.
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