Geodesic
Some Mean-Value Theorems of the Cauchy Type
Fractional calculus and applied analysis, Tome 9 (2006) no. 2, pp. 143-158.

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Some mean-value theorems of the Cauchy type, which are connected with Jensen’s inequality, are given in [2] in discrete form and in [5] in integral form. Several further generalizations and applications of these results are presented here.
Keywords: Mean-Value Theorems, Jensen’s Inequality, Quasi-Arithmetic Mean, Power Mean, Tobey Mean, Stolarsky-Tobey Mean, Functional Stolarsky Mean, Symmetric Mean, Whiteley Mean, 26A24, 26D15, 41A05 
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Pecaric, Josip; Rodic Lipanovic, Mirna; Srivastava, H. M. Some Mean-Value Theorems of the Cauchy Type. Fractional calculus and applied analysis, Tome 9 (2006) no. 2, pp. 143-158. http://geodesic.mathdoc.fr/item/FCAA_2006_9_2_a3/