International Journal of Mathematics and Mathematical Sciences 
Volume 2003 (2003), Issue 50, Pages 3171-3187
doi:10.1155/S0161171203210486

The additive approximation on a four-variate Jensen-type operator equation

Jian Wang1,2

 1Department of Mathematics, Nanjing University, Nanjing 210093, China
2Department of Mathematics, Fujian Normal University, Fuzhou 350007, China
Received 27 October 2002

Abstract

We study the Hyers-Ulam stability theory of a four-variate Jensen-type functional equation by considering the approximate remainder ϕ and obtain the corresponding error formulas. We bring to light the close relation between the β-homogeneity of the norm on F∗-spaces and the approximate remainder ϕ, where we allow p,q,r, and s to be different in their Hyers-Ulam-Rassias stability.