The Hyers–Ulam stability of an additive-quadratic s-functional inequality in Banach spaces.

For any fixed s ∈ z ∈ C : z ≠ 0 and | z | < 1 , we consider the following functional inequality: 1 ‖ f (a + a ′ , c + c ′) + f (a + a ′ , c - c ′) + f (a - a ′ , c + c ′) + f (a - a ′ , c - c ′) - 4 f (a , c) - 4 f (a , c ′) ‖ ≤ ‖ s (2 f a + a ′ , c - c ′ + 2 f a - a ′ , c + c ′ - 4 f (a , c) - 4 f (a , c ′) + 4 f (a ′ , c ′)) ‖. In this paper, we obtain the Hyers–Ulam stability of the proposed functional inequality using the direct and fixed point methods. [ABSTRACT FROM AUTHOR]