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

Abstract

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 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