engleski

On the properties of McShane's functional and their applications

In this paper we derive some remarkable properties of McShane's functional, defined by means of positive isotonic linear functional. These properties are then applied to weighted generalized means. Series of consequences among additive and multiplicative type mean inequalities is given, as well as a special consideration of Holder's inequality, in view of the new results.

inequalities ; convex functions ; Jensen's inequality ; Jessen's functional ; McShane's functional ; superadditivity ; subadditivity ; monotonicity ; weighted generalized means ; additive inequalities ; multiplicative inequalities ; Holder type inequalities ; Minkowski type inequalities ; quasiarithmetic means ; n-convexity

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