A New Approach to Hyers-Ulam Stability of r-Variable Quadratic Functional Equations

Abstract

In this paper, we investigate the general solution of a new quadratic functional equation of the form ∑1≤i<j<k≤rϕli+lj+lk=r−2∑i=1,i≠jrϕli+lj+−r2+3r−2/2∑i=1rϕli. We prove that a function admits, in appropriate conditions, a unique quadratic mapping satisfying the corresponding functional equation. Finally, we discuss the Ulam stability of that functional equation by using the directed method and fixed-point method, respectively.