Times: 2025 Feb 28 from 03:00PM to 03:15PM (Eastern Time (US & Canada))
Abstract:
While studying some inequalities of fractions, we encounters a new value. For fractions $\frac{a_1}{b_1}, \frac{a_2}{b_2}, \cdots, \frac{a_n}{b_a}$, we define this new value by: $\bar{m}=\frac{a_1+\cdots+a_n}{b_1+\cdots+b_n}$. It can be proved that this value is bounded between the maximum and the minimum of these fractions, like all other means. In this talk, we will compare this value with one of the most commonly used means, the Arithmetic Mean, and introduce some properties of this new value.