engleski

Cauchy-type means for signed measures

Some mean-value theorems of the Cauchy type, which are connected with Jensen's inequality, are given in [A.McD.Mercer: Some new inequalities involving elementary mean values, J.Math.Anal.Appl. 229 (1999), 677-681.] in discrete form and in [J.E.Pečarić, I.Perić, H.M.Srivastava: A family of the Cauchy type mean-value theorems, J.Math.Anal.Appl.306 (2005), 730-739.] in integral form. Using the generalization of these results for some signed measures, here we define some new means of the Cauchy type for such measure. Monotonicity of these new means is also discussed.

mean-value theorem; Jensen's inequality; means; signed measure

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