engleski

A refinement of the Jessen-Mercer inequality and a generalization on convex hulls in R^{; ; ; k}; ; ;

We present a refinement of the Jessen-Mercer inequality and use it to improve an upper bound for the Jessen's difference. Also, we present a generalization of the Jessen-Mercer inequality for convex functions on convex hulls in R^{; ; ; k}; ; ; . We apply an elegant method of producing n- exponentially convex and exponentially convex functions using the Jessen-Mercer differences. We prove Cauchy mean value type theorems and show them to be useful in studying Stolarsky type means defined by using the Jessen-Mercer differences.

Jessen-Mercer inequality; convex functions; convex hulls; n-exponential convexity; Stolarsky type means

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