BOHR’S INEQUALITIES IN n-INNER PRODUCT SPACES

Cheung, W.S.; Cheung, W.S.; Cho, Y.S.; Cho, Y.S.; Pecaric, J.; Pecaric, J.; Zhao, D.D.; Zhao, D.D.

P-ISSN1226-0657
E-ISSN2287-6081
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Vol.14 No.2

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BOHR’S INEQUALITIES IN n-INNER PRODUCT SPACES

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081

2007, v.14 no.2, pp.127-137

Cheung, W.S.
Cho, Y.S.
Pecaric, J.
Zhao, D.D.

Cheung,, W. , Cho,, Y. , Pecaric,, J. , & Zhao,, D. (2007). BOHR’S INEQUALITIES IN n-INNER PRODUCT SPACES. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 14(2), 127-137.

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Abstract

The classical Bohr's inequality states that <TEX>$|z+w|^2{\leq}p|z|^2+q|w|^2$</TEX> for all <TEX>$z,\;w{\in}\mathbb{C}$</TEX> and all p, q>1 with <TEX>$\frac{1}{p}+\frac{1}{q}=1$</TEX>. In this paper, Bohr's inequality is generalized to the setting of n-inner product spaces for all positive conjugate exponents <TEX>$p,\;q{\in}\mathbb{R}$</TEX>. In. In particular, the parallelogram law is recovered and an interesting operator inequality is obtained.

keywords: Bohr's inequality, n-inner product space, n-normed linear space

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Article Contents

Vol.14 No.2

BOHR’S INEQUALITIES IN n-INNER PRODUCT SPACES

Abstract

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics