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On a refinement of the Majorisation type inequality

Adil Khan M., Niezgoda M., Pečarić J.

Demonstratio Mathematica

2011

Vol. 44, nr 1

49-57

In this note, two mean value theorems are proved by using some recent results by Barnett et al. [N. S. Barnett, P. Cerone, S. S. Dragomir, Majorisation inequalities for Stieltjes integrals, Appl. Math. Lett. 22 (2009), 416-421]. A new class of Cauchy type means for two functions is studied. Logarithmic convexity for differences of power means is proved. Monotonicity of Cauchy means is shown.

Integral inequalities of Hadamard type for log-convex functions

Dragomir S., Mond B.

Demonstratio Mathematica

1998

Vol. 31, nr 2

355-364

In this paper, we derive some integral inequalities for log-convex functions which are closely connected with the classical inequality due to Hermite-Hadamard.