Generalizations of Sherman’s inequality by Lidstone’s interpolating polynomial

Abstract

In majorization theory, the well-known majorization theorem plays a very important role. A more general result was obtained by Sherman. In this paper, concerning 2n-convex functions, we get generalizations of these results applying Lidstone's interpolating polynomials and theČebyšev functional. Using the obtained results, we generate a new family of exponentially convex functions. The results are some new classes of two-parameter Cauchy type means. MSC: 26D15

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