文摘
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 the Čebyšev 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. Keywords majorization n-convexity Schur-convexity Sherman’s theorem Lidstone interpolating polynomial Čebyšev functional Grüss type inequalities Ostrowsky type inequalities exponentially convex functions log-convex functions means