An optimal double inequality between geometric and identric means

作者：Wang, Miao-Kun; Wang, Zi-Kui; Chu, Yu-Ming^*

来源：Applied Mathematics Letters, 2012, 25(3): 471-475.

DOI：10.1016/j.aml.2011.09.038

• Geometric mean
• Identric mean
• Inequality

We find the greatest value p and least value q in (0, 1/2) such that the double inequality G(pa + (1 - p)b, pb + (1 - p)a) < I(a, b) < G(qa + (1 - q)b, qb + (1 - q)a) holds for all a, b > 0 with a not equal b. Here, G(a, b), and 1(a, b) denote the geometric, and identric means of two positive numbers a and b, respectively.

• 出版日期2012-3
• 单位杭州师范大学; 湖州师范学院