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 [4],[5]. Applying so called exp-convex method established in [8],[9], 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 [2].