engleski

Some mean-value theorems of the Cauchy type

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. Several further generalizations and applications of these results are presented here.

Mean-value theorems; Jensen's inequality; quasi-arithmetic mean; power mean; Tobey mean; Stolarsky-Tobey mean; functional Stolarsky mean; symmetric mean; Whiteley mean

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