Hyers-Ulam stability of a-type additive functional equations in Banach space using direct method

In this paper, we introduce the new kind of a-type additive functional equation and investigate the Hyers-Ulam stability of a-type additive functional equations within the Banach spaces using the direct method.This approach provides a straightforward and efficient way to establish the stability of functional equations without relying on more complex or indirect techniques.We begin by defining the specific a-type additive functional equation under consideration and outlining the conditions required for its stability.Through rigorous mathematical analysis, we demonstrate that under certain constraints, the functional equation exhibits Hyers-Ulam stability.