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Classical and New Inequalities in Analysis pp 559–594Cite as

More on Norm Inequalities

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Part of the book series: Mathematics and Its Applications () ((MAEE,volume 61))

Abstract

H. Xu and Z. Xu [1] claimed the following inequality in L p (1 < p < 2):

$${\left( {\left. {\parallel \lambda x + \mu y{\parallel ^2} + g\left( \mu \right)\parallel x - y{\parallel ^2}} \right)} \right.^{1/2}}{\left( {\lambda \parallel x{\parallel ^p} + \mu \parallel y{\parallel ^p}} \right)^{1/p}}$$
(1.1)

where x,y ∈ L p, 0 ≤ µ ≤ 1, λ = 1 − µ, in the case when the function g is given by g(µ) = µ λ(p − 1).

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Authors and Affiliations

  1. University of Belgrade, Belgrade, Yugoslavia

    D. S. Mitrinović

  2. University of Zagreb, Zagreb, Croatia

    J. E. Pečarić

  3. Department of Mathematics, Iowa State University of Science and Technology, Ames, Iowa, USA

    A. M. Fink

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  1. D. S. Mitrinović
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Mitrinović, D.S., Pečarić, J.E., Fink, A.M. (1993). More on Norm Inequalities. In: Classical and New Inequalities in Analysis. Mathematics and Its Applications (East European Series), vol 61. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1043-5_19

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