## Abstract

Let F(u, v) be a symmetric real function defined for α<u, v<β and assume that G(u, v, w)=F(u, v)+F(u, w)-F(v, w) is decreasing in v and w for u≦min (u, v). For any set (y)=(y_{ 1}, ..., y_{ n} ), α<y_{ i} <β, given except in arrangement Σ_{ i}^{ =1/n} F(y_{ i}, y_{ i+1}) where y_{ n+1}=y_{ 1}) is maximal if (and under some additional assumptions only if) (y) is arranged in circular symmetrical order. Examples are given and an additional result is proved on the product Π_{ i}^{ =1/n} [(y2 i-1 y2 i)^{ m} +α_{ 1}(y_{ 2 i-1} y_{ 2 i} )^{ m-1}+ ... +a_{ m} ] where a_{ k} ≧0 and where the set (y)=(y_{ 1}, .., y_{ n} ), y_{ i} ≧0 is given except in arrangement. The problems considered here arose in connection with a theorem by A. Lehman [1] and a lemma of Duffin and Schaeffer [2].

Original language | English |
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Pages (from-to) | 177-181 |

Number of pages | 5 |

Journal | Israel Journal of Mathematics |

Volume | 5 |

Issue number | 3 |

DOIs | |

State | Published - Jul 1967 |

Externally published | Yes |

## ASJC Scopus subject areas

- Mathematics (all)

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