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On exponential convexity, Jensen-Steffensen-Boas Inequality, and Cauchy's means for superquadratic functions

In this paper we define new means of Cauchy's type using some recently obtained results that refine the Jensen-Steffensen-Boas inequality for convex and superquadratic functions. Applying so called exp-convex method we interpret results in the form of exponentially convex or (as a special case) logarithmically convex functions. We also present some related results which generalize results in <cite>AFP</cite>.

Jensen-Steffensen inequality; superquadratic functions; Cauchy Means; Monotonicity; exponential convexity; log-convexity

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