Sharp bounds for the difference between the arithmetic and geometric means

Abstract

We present sharp bounds for ${\sum }_{i=1}^n{\alpha }_i{x}_i-{\prod }_{i=1}^n{x}_i^{{\alpha }_i}$ in terms of the variance of the vector $(x_1^{1/2},...,x_n^{1/2})$.

7 pages

References in corpus (4)

• A stability version of Hölder's inequality
• Concentration of the ratio between the geometric and arithmetic means
• Selfimprovemvent of the inequality between arithmetic and geometric means
• A refinement of the inequality between arithmetic and geometric means

Cited by in corpus (1)

• A monotonicity property of variances