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BOHR’S INEQUALITIES IN n-INNER PRODUCT SPACES
W. S. Cheung,조열제,J. Peˇcari´c,D. D. Zhao 한국수학교육학회 2007 純粹 및 應用數學 Vol.14 No.2
The classical Bohr's inequality states that |z + w|2 ≤p|z|2 + q|w|2 for all z,w∈C and all p,q > 1 with 1/p +1/q = 1. In this paper, Bohr's inequality is generalized to the setting of n-inner product spaces for all positive conjugate expo-nents p,q∈R. In particular, the parallelogram law is recovered and an interesting operator inequality is obtained.