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

Abstract

For any fixed s is an element of {z is an element of C : z not equal 0 and vertical bar z vertical bar < 1}, we consider the following functional inequality: parallel to f(a + a', c + c') + f(a + a', c - c') + f(a - a', c + c') + f(a - a', c - c')-4f(a, c) - 4f(a, c')parallel to <= parallel to s(2f(a + a', c - c') +2f(a-a', c+c')-4f(a, c) - 4f(a, c') + 4f(a', c'))parallel to. (1) In this paper, we obtain the Hyers-Ulam stability of the proposed functional inequality using the direct and fixed point methods.