Applications of convexity on quantities and inequalities (Q2844381)

The paper deals with geometrical and physical applications of convexity and functional inequalities. By using of means and integrals on \(\mathbb R^2\) or \(\mathbb R^3\) it is proved that the center of nonnegative quantity can be reduced to the geometric center of a convex set (cf. Theorems 4.2, 4.3). Finally, it is reminded that the convexity of real functions can be characterized by discrete and integral Jensen inequalities (Theorems E, F, cf. also [\textit{Z. Pavić, J. Pečarić} and \textit{I. Perić}, J. Math. Inequal. 5, No. 2, 253--264 (2011; Zbl 1220.26016)]).