Some results on extending and sharpening the Weierstrass product inequalities

In this paper, we establish two extensions of Weierstrass’s inequality involving symmetric functions by means of the theory of majorization, and give an interesting sharpness of Weierstrass’s inequality by using the arithmetic–geometric mean inequality. Furthermore, we apply these results to improve a well-known inequality and deduce some new inequalities.  2004 Elsevier Inc. All rights reserved