On some new generalizations of Hua's inequality (Q2226633)

The aim of the authors is to give a generalization of the inequality proved by \textit{L. K. Hua} [Additive theory of prime numbers. American Mathematical Society (AMS), Providence, RI (1965; Zbl 0192.39304)] for the \(C^*\)-valued norm due to \textit{M. S. Moslehian} [Linear Algebra Appl. 430, No. 4, 1131--1139 (2009; Zbl 1179.47018)] in the setting of Hilbert \(C^*\)-modules using neither convexity nor the classical Hua inequality. \par As its applications, some known and new generalizations of inequality proved by Hua are deduced.\par Also, the authors establish the connection between \(C^*\)-valued norm triangle inequality and \(C^*\)-valued norm inequality proved by Hua. \par Moreover, the authors entirely devote a part of the paper to the study of some operator versions of Hua's inequality on Hilbert spaces involving operator convex function and positive mappings. \par Finally, they obtain various forms of the inequaliy proved by Hua.