The increase of sums and products dependent on (y 1, …,y n ) by rearrangement of this set |
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Authors: | Abramovich Shoshana |
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Institution: | (1) Technion-Israel Institute of Technology, Haifa, Israel |
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Abstract: | LetF(u, v) be a symmetric real function defined forα<u, v<β and assume thatG(u, v, w)=F(u, v)+F(u, w)−F(v, w) is decreasing inv andw foru≦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) wherey
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 productΠ
i
=1/n
(y2i−1y2i)
m
+α
1(y
2i−1
y
2i
)
m−1+ … +a
m
] wherea
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].
This paper is part of the author’s Master of Science dissertation at the Technion-Israel Institute of Technology.
The author wishes to thank Professor B. Schwarz and Professor E. Jabotinsky for their help in the preparation of this paper. |
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Keywords: | |
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