Hyers–Ulam Stability of Additive Functional Equation Using Direct and Fixed-Point Methods

Abstract

In this present work, we obtain the solution of the generalized additive functional equation and also establish Hyers–Ulam stability results by using alternative fixed point for a generalized additive functional equation χ∑g=1lvg=∑1≤g<h<i≤lχvg+vh+vi−∑1≤g<h≤lχvg+vh−l2−5l+2/2∑g=1lχvg−χ−vg/2. where l is a nonnegative integer with ℕ−0,1,2,3,4 in Banach spaces.