THE ADDITIVE APPROXIMATION ON A SIX-VARIATE JENSEN TYPE OPERATOR EQUATION

Abstract

The concept of the Hyers-Ulam stability is a special case of the generalized concept: Hyers-Ulam-Rassias stability that was originated from the innovative approach of Rassias that appeared in Rassias [13]. We focus our attention here mainly on the Hyers-Ulam stability of a 6-variate Jensen type functional equation. Taking into account the property of the approximate remainder phi, we derive some important conclusions and the corresponding error formulas. Under the assumption that every pi for i = 1, 2, ..., 6 is different from each other, we link up the beta-homogeneity of the norm on F*-spaces with phi. In particular, we make sure pi's area whether the Hyers-Ulam stability is affirmative or negative.