We present new generalizations of the weighted Montgomery identity constructed by using the Hermite interpolating polynomial. The obtained identities are used to establish new generalizations of weighted Ostrowski type inequalities for differentiable functions of class $C^{n}$ . Also, we consider new bounds for the remainder of the obtained identities by using the Chebyshev functional and certain Grüss type inequalities for this functional. By applying those results we derive inequalities for the class of n-convex functions.

中文翻译：

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通过Hermite多项式推广Ostrowski型不等式

我们介绍了通过使用Hermite插值多项式构造的加权Montgomery身份的新概括。所获得的恒等式用于为类$ C ^ {n} $的可微函数建立加权Ostrowski型不等式的新概括。另外，我们通过使用切比雪夫（Chebyshev）函数和该函数的某些Grüss型不等式，来考虑获得的其余身份的新边界。通过应用这些结果，我们得出n凸函数类的不等式。