A remark on the Lo-Keng Hua inequality
The authors obtain generalizations of Lo-Keng Hua's inequality [see \textit{L.-K. Hua}: ``Additive theory of prime numbers'' (1965; Zbl 0192.39304)]. Main result: Let \(f: {\mathcal T}\to \mathbb{R}\) be a convex function and let \(\alpha\), \(\delta\), \(x_1,\dots, x_n\) be real numbers such that \(\alpha> 0\) and \(\delta- x_1-\cdots- x_n\), \(\alpha x_1,\dots, \alpha x_n\in {\mathcal T}\). Then \[ f(\delta- x_1-\cdots- x_n)+ \sum^n_{i= 1} \alpha^{- 1} f(\alpha x_i)\geq {\alpha+ n\over n} f\Biggl({\alpha \delta\over \alpha+ n}\Biggr). \] For \(f(x)= x^2\) it results Lo-Keng Hua's inequality. A similar generalization is given for the integral Lo-Keng Hua's inequality [see \textit{C.-L. Wang}, J. Math. Anal. Appl. 166, No. 2, 345-350 (1992; Zbl 0756.26014)].
scientific article; zbMATH DE number 710348