Advances in Difference Equations
Volume 2011 (2011), Article ID 617564, 9 pages
doi:10.1155/2011/617564
Research Article

Solution to a Function Equation and Divergence Measures

Chuan-Lei Dong and Jin Liang

Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China

Received 1 January 2011; Accepted 11 February 2011

Academic Editor: Toka Diagana

Copyright © 2011 Chuan-Lei Dong and Jin Liang. 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.

Abstract

We investigate the solution to the following function equation 𝑓 1 ( 𝑥 ) 𝑔 1 ( 𝑦 ) + ⋯ + 𝑓 𝑛 ( 𝑥 ) 𝑔 𝑛 ( 𝑦 ) = 𝐺 ( 𝑥 + 𝑦 ) , which arises from the theory of divergence measures. Moreover, new results on divergence measures are given.