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

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.