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On Hadamard’s inequality for the convex mappings defined on a ball in the space and applications. (English) Zbl 0951.26010

The author proves an inequality of Hadamard type for real-valued convex functions on a ball in \(\mathbb{R}^3\). Some mappings naturally connected with this inequality are considered and their properties (monotonicity, convexity, bounds) are investigated.

MSC:

26D15 Inequalities for sums, series and integrals
26B25 Convexity of real functions of several variables, generalizations
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