Abstract
For x [0, 1]n with 1 = 1 and y ∈ [1, ∞)n, we prove that $$\frac{\Vert\textit{\ textbf{xy}}\Vert-{\infty}}{\Vert\textit{\textbf{xy}}\Vert-{2}} \le \Vert\textit{\textbf{x}}\Vert-{\infty} \Vert\textit{\textbf{y}}\Vert-{1} \frac{\Vert\textit{\textbf{y}}\Vert-{\infty}}{\Vert\textit{\textbf{y}}\Vert-{2}} $$, where xy n is the vector with components x iyi. This bound does not seem to easily follow from known inequalities, and the proof technique may be of independent interest.
Original language | English |
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Article number | 1350026 |
Pages (from-to) | 1-5 |
Journal | Analysis and Applications |
Volume | 11 |
Issue number | 6 |
DOIs | |
State | Published - 1 Nov 2013 |
Keywords
- Vector
- inequalities
- norm
ASJC Scopus subject areas
- Analysis
- Applied Mathematics