INEQUALITIES FOR THE RATIOS OF THE MEAN VALUES OF FUNCTIONS

Abstract

In the article, some inequalities for the ratios of the mean values of functions are obtained and an open problem posed by B.-N. Guo and F. Qi in [An inequality between ratio of the extended logarithmic means and ratio of the exponential means, Taiwanese J. Math. 7(2) (2003), 229-237 and [An algebraic inequality, II, RGMIA Res. Rep. Coll. 4(8) (2001), 55{61. is solved affirmatively. In the final, two new open problems are posed by the first author.