... “Generalization and sharpness of the power means inequality and their applications, ”Journal of Mathematical Analysis and Applications, vol. 312, no. 2, pp. 637–652, 2005.20 P. S. Bullen, A Dictionary of ... eigenvalues of a linear transformation,” Proceedings of the National Academy of Sciences of the United States of America, vol. 35, pp. 408–411, 1949.Journal of Inequalities and Applications ... follows from Cases 1–4 and the proof of Theorem 3.4 is completed.4. Applications In this section, we establish some inequalities by use of Theorems 3.1, 3.2 and 3.4 and thetheory of majorization.Theorem...