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Improvements of the Giaccardi and the Petrović inequality and related Stolarsky type means

Improvements of the Giaccardi and the Petrović inequality are given. The notion of n-exponentially convex functions is introduced. An elegant method of producing n-exponentially convex and exponentially convex functions is applied using the Giaccardi and the Petrović differences. Cauchy mean value theorems are proved and shown to be useful in studying Stolarsky type means defined by using the Giaccardi and the Petrović differences.

Giaccardi inequality; Petrović inequality; Cauchy type mean value theorems; n-exponential convexity; exponential convexity; Stolarsky type means

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