On a Mixed Arithmetic-Mean, Geometric-Mean, Harmonic-Mean Inequality

In 1992, F. Holland [1] conjectured the following mixed arithmetic-mean, geometric-mean inequality: Where x1, x2, …, xn are positive real numbers with equality if and only if x1 = x2 = … = xn. And K. Kedlaya [2] proved it in 1994. We can extend this inequality, and the purpose of this paper is to address it.