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A generalization of Young's $L^p$ inequality

Borwein, Jonathan M. (1997) A generalization of Young's $L^p$ inequality. Mathematical Inequalities and Applications, 1 . pp. 131-136.

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      Abstract

      We show that, for positive real numbers with $a \ge 1+ \sum_i^N \alpha_i$, the function $${r^a \over{a}} \over{ \prod_{i=1}^N x_i^{\alpha_i}}$$ has a convex conjugate of the same form and so, in particular, obtain a clean proof that $f$ is convex.

      Item Type: Article
      Additional Information: pubdom FALSE
      Uncontrolled Keywords: Fenchel conjugate, Young $\ell^p$-inequality, convexity
      Subjects: 90-xx Economics, operations research, programming, games > 90Cxx Mathematical programming
      52-xx Convex and discrete geometry > 52Axx General convexity
      26-xx Real functions > 26Axx Functions of one variable
      Faculty: UNSPECIFIED
      Depositing User: Users 1 not found.
      Date Deposited: 25 Nov 2003
      Last Modified: 13 Jan 2015 16:53
      URI: https://docserver.carma.newcastle.edu.au/id/eprint/189

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