engleski

Generalizations of Sherman's inequality

The concept of majorization is a powerful and useful tool which arises frequently in many different areas of research. Together with the concept of Schur-convexity it gives an important characterization of convex functions. A very important role in majorization theory plays the well known Majorization theorem which gives a relation between one-dimensional convex functions and n-dimensional Schur-convex functions. More general result was obtained by S. Sherman. In this paper, we get generalizations of these results for n-convex functions using Taylor's interpolating polynomial and Čebyšev functional. We apply Exponentiallly convex method in order to interpret our results in the form of exponentially or in the special case logarithmically convex functions. The outcome are some new classes of two-parameter Cauchy-type means.

majorization ; n-convexity ; Schur-convexity ; Sherman's theorem ; Taylor interpolating polynomial ; Čebyšev functional ; Grüss type inequalities ; Ostrowsky-type inequalities ; exponentially convex functions ; log-convex functions ; means

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