engleski

On Jensen's inequality involving averages of convex functions

Using Wulbert result from [18] we deduce a method for constructing exponentially convex functions. To this date there is no known operative criteria for recognizing exponentially convex functions, so our method is of a special interest since there is a lack of examples of this class of functions. Constructed exponentially convex functions are then used for the construction of two and three parameters Cauchy means, that have the very nice property: they have the monotonicity property in their defining parameters. Particularly, we generalize recent results on Cauchy means from [2] and [4].

Jensen’s inequality; log-convex function; exponential convexity

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