engleski

Cauchy-type means for positive linear functionals

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 and H. M. Srivastava, A family of the Cauchy type mean-value theorems, J. Math. Anal. Appl., 306 (2005), 730-739.] in integral form. Here we give the generalization of that result for positive linear functionals. Using that result, newmeans of Cauchy type for positive linear functionals are given. Monotonicity of these newmeans is also discussed.

Jensen’s inequality; mean-value theorems; linear functional; generalized means; generalized power mean; Cauchy-type means

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