On a particular extension of the EV-Theorem

Cîrtoaje, Vasile and Giugiuc, Leonard

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creative_2022_31_2_173_184

DOI: https://doi.org/10.37193/CMI.2022.02.03

Issue no: Vol 31/2022 no. 2 Tags: EV-Theorem, maximum product, minimum product, fixed sums

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The main aim of the paper is to determine the extreme values of the product $P=a_1a_2\cdots a_n$ under the constraints $\sum_{i=1}^n a_i=S$ and $\sum_{i=1}^{n}\frac 1{a_i+1}=S_0$ for $n\ge 3$ nonnegative real numbers $a_1,a_2,\ldots, a_n$ and some given constants $S$ and $S_0$ . Some interesting applications of our results are provided as well.