International Journal of Mathematics and Mathematical Sciences
Volume 28 (2001), Issue 7, Pages 419-425
A generalization of Ky Fan's inequality
Department of Mathematics, University of Michigan, 2074 East Hall, 525 East University Avenue, Ann Arbor 48109, MI, USA
Received 20 March 2001; Revised 17 July 2001
Copyright © 2001 Peng Gao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Let be the generalized weighted means. Let be a function, an implicit decreasing function
defined by and , , , . Then for , if , A similar result exists for . By specifying and , we get various generalizations of Ky Fan's inequality. We also present some results on the comparison of and for , .