26D15.

Recently Feng Qi has presented a sharp inequality between the sum of squares and the exponential of the sum of a nonnegative sequence. His result has been extended to more general power sums by Huan-Nan Shi, and, independently, by Yu Miao, Li-Min Liu, and Feng Qi. In this note we generalize those inequalitites by introducing weights and permitting more general functions. Inequalities in the opposite direction are also presented.;