Convex? (Solved)

Summary: For each $N \in \NN$ define the function $f_N: \RR_+^N \to \RR_+$ by $f_N(x_1, \ldots, x_N) := \int_0^1 (1 - \prod_{i=1}^N (1-t^{x_i})) dt/t$. It is desired to know whether $f_N$ is convex.

Classification: Primary, classical analysis; Secondary, convex functions

• Download Problem [PDF]
  
  Jonathan Borwein
  CECM
  Department of Mathematics and Statistics
  Simon Fraser University
  Burnaby, BC, V5A 1S6
  Canada
  e-mail: [email protected]
  
  Ian Affleck
  CECM
  Simon Fraser University
  
  Roland Girgensohn
  GSF-Forshungszentrum
  Institut für Biomathematik und Biometrie
  Neuherberg, Germany
  
  
• Download Solution [PDF]
  
  Ian Affleck
  CECM
  Department of Mathematics and Statistics
  Simon Fraser University
  Burnaby, BC, V5A 1S6
  Canada
  e-mail: [email protected]
  
  
• Download Solution [PDF]
  
  Jonathan Borwein
  CECM
  Department of Mathematics and Statistics
  Simon Fraser University
  Burnaby, BC, V5A 1S6
  Canada
  e-mail: [email protected]
  
  Omar Hijab
  Department of Mathematics
  Temple University
  Philadelphia, PA 19122, USA
  e-mail: [email protected]

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