A refinement of the Jessen-Mercer inequality and a generalization on convex hulls in ?<SUP>k</SUP>

A. Matkovi?; J. Pe?ari?; J. Peri?

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A refinement of the Jessen-Mercer inequality and a generalization on convex hulls in ?^k

机译：Jessen-Mercer不等式的细化和？^{k 中凸包的推广}

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Arefinement of the Jessen-Mercer inequality is obtained and shown to be an improve- ment of the upper bound for the Jessen's difference given in [ 12 ]. Also a generalization of the Jessen-Mercer inequality for convex functions on convex hulls in R k is given and demon- strated to be an improvement of the inequalities obtained in [ 3 ]. An elegant method of producing n -exponentially convex and exponentially convex functions is applied using the Jessen-Mercer differences. Lagrange and Cauchy mean value type theorems are proved and shown to be useful in studying Stolarsky type means defined by using the Jessen-Mercer differences.

机译：获得Jessen-Mercer不等式的细化，并证明这是对[12]中给出的Jessen差的上限的改进。还给出了R k中凸壳上凸函数的Jessen-Mercer不等式的一般化，并证明是对[3]中获得的不等式的改进。利用Jessen-Mercer差应用产生n-指数凸函数和指数凸函数的一种优雅方法。证明了Lagrange和Cauchy均值类型定理，并证明它们对研究使用Jessen-Mercer差定义的Stolarsky型均值有用。

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《Journal of Mathematical Inequalities》 |2015年第4期|共22页
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A. Matkovi?; J. Pe?ari?; J. Peri?;
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A refinement of the Jessen-Mercer inequality and a generalization on convex hulls in ?k

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A refinement of the Jessen-Mercer inequality and a generalization on convex hulls in ?^k