Abstract
This manuscript develops the study of reverse Hilbert-type inequalities by applying reverse Holder inequalities on T. We generalize the reverse inequality of Hilbert-type with power two by replacing the power with a new power beta, beta > 1. The main results are proved by using Specht's ratio, chain rule and Jensen's inequality. Our results (when T = N) are essentially new. Symmetrical properties play an essential role in determining the correct methods to solve inequalities.