ON STABILILTY OF GENERALIZED ADDITIVE FUNCTIONAL EQUATIONS IN BANACH SPACE

Abstract

The stability problem arises when a functional equation is replaced by an inequality. When the equation admits a unique solution, we say that the equation is stable. In this paper, an Arunkumar-Agilan type additive functional equation is considered. By applying the direct method introduced by Hyers and the method of Gavruta, we established the Hyers-Ulam-Rassias stability condition for such an additive functional equation.

Keywords

• banach space
• hyers-ulam-rassias stability
• functional equation