In this paper, we solve the following bi-additive s-functional inequalities ‖ f (x + y, z + w) + f (x + y, z − w) + f (x − y, z + w) + f (x − y, z − w) − 4 f (x, z)‖ ≤ ∥∥∥s (2 f (x + y, z − w) + 2 f (x − y, z + w) − 4 f (x, z) + 4 f (y,w))∥∥∥ (1) and ∥∥∥2 f (x + y, z − w) + 2 f (x − y, z + w) − 4 f (x, z) + 4 f (y,w)∥∥∥ (2) ≤ ∥∥∥s ( f (x + y, z + w) + f (x + y, z − w) + f (x − y, z + w) + f (x − y, z − w) − 4 f (x, z))∥∥∥ , where s is a fixed nonzero complex number with |s| < 1. Moreover, we prove the Hyers-Ulam stability of biderivations and bihomomorphismsions in Banach algebras and unital C∗-algebras, associated with the bi-additive s-functional inequalities (1) and (2)