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  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

ISSN : 1226-0657

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Vol.14 No.2

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BOHR'S INEQUALITIES IN n-INNER PRODUCT SPACES

BOHR’S INEQUALITIES IN n-INNER PRODUCT SPACES

한국수학교육학회지시리즈B:순수및응용수학 / 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. (DEPARTMENT OF MATHEMATICS, THE UNIVERSITY OF HONG KONG)
Cho, Y.S. (DEPARTMENT OF MATHEMATICS EDUCATION AND THE RINS, GYEONGSANG NATIONAL UNIVERSITY)
Pecaric, J. (FACULTY OF TEXTILE TECHNOLOGY, UNIVERSITY OF ZAGREB)
Zhao, D.D. (DEPARTMENT OF MATHEMATICS, THE UNIVERSITY OF HONG KONG)
Cheung, W.S., Cho, Y.S., Pecaric, J., & Zhao, D.D.. (2007). BOHR'S INEQUALITIES IN n-INNER PRODUCT SPACES. 한국수학교육학회지시리즈B:순수및응용수학, 14(2), 127-137.

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

한국수학교육학회지시리즈B:순수및응용수학

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