Cheung, W. S.; Cho, Y. J.; Pečarić, J.; Zhao, D. D. Bohr’s inequalities in \(n\)-inner product spaces. (English) Zbl 1185.46012 J. Korea Soc. Math. Educ., Ser. B, Pure Appl. Math. 14, No. 2, 127-137 (2007). The classical Bohr inequality states that, for any \(z, w\in \mathbb C\) and conjugate exponents \(p,q >1\), \(|z + w|^2\leq p|z|^2 + q|w|^2\).In the past few decades, various generalizations of this inequality have been obtained [W.-S.Cheung and J.Pečarić, J. Math.Anal.Appl.323, No.1, 403–412 (2006; Zbl 1108.26018); O.Hirzallah, J. Math.Anal.Appl.282, No.2, 578–583 (2003; Zbl 1028.47009)], without restriction to the conjugate components \(p,q\).Here, Bohr’s inequality is generalised to the context of \(n\)-inner-product spaces for all positive conjugate exponents \(p, q\). As an application of these Bohr-type inequalities, an interesting inequality on operators in an \(n\)-inner product space is presented. In particular, the parallelogram law is recovered. Reviewer: V. Lokesha (Bangalore) Cited in 1 Document MSC: 46C50 Generalizations of inner products (semi-inner products, partial inner products, etc.) 47A30 Norms (inequalities, more than one norm, etc.) of linear operators 26D15 Inequalities for sums, series and integrals 30A10 Inequalities in the complex plane Keywords:Bohr’s inequality; \(n\)-inner product spaces; paralleogram law Citations:Zbl 1108.26018; Zbl 1028.47009 PDFBibTeX XMLCite \textit{W. S. Cheung} et al., J. Korean Soc. Math. Educ., Ser. B, Pure Appl. Math. 14, No. 2, 127--137 (2007; Zbl 1185.46012)