On Some Inequalities in Normed Linear Spaces

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Dragomir, Sever S (2007) On Some Inequalities in Normed Linear Spaces. Research report collection, 10 (Supp).


Upper and lower bounds for the norm of a linear combination of vectors are given. Applications in obtaining various inequalities for the quantities ||x/||x|| - y/||y|| || and ||x/||y|| - y/||x|| ||, where x and y are nonzero vectors, that are related to the Massera-Schäffer and the Dunkl-Williams inequalities are also provided. Some bounds for the unweighted Čebyšev functional are given as well.

Item type Article
URI https://vuir.vu.edu.au/id/eprint/18005
Subjects Historical > FOR Classification > 0101 Pure Mathematics
Current > Collections > Research Group in Mathematical Inequalities and Applications (RGMIA)
Keywords normed linear spaces, triangle inequality, Massera-Schäffer inequality, Dunkl-Williams inequality, Čebyšev functional
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