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Note on an inequality of Gauss (CROSBI ID 171847)
Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija
Pečarić, Josip ; Smoljak, Ksenija
Note on an inequality of Gauss // Journal of mathematical inequalities, 5 (2011), 2; 199-211
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Pečarić, Josip ; Smoljak, Ksenija
engleski
Note on an inequality of Gauss
In this paper a functional defined as the difference between the left-hand and the right-hand side of an extension of the Gauss inequality given in [H. Alzer, On an inequality of Gauss, Rev. Mat. Complut. 4(2) (1991), 179–183.] is studied. Related analogous of the Lagrange and the Cauchy mean value theorems are obtained. Furthermore, Gauss means are generated and their monotonicity property is proven.
Gauss inequality; mean value theorems; exponential convexity; means
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