Ulam stability of a quadratic-type functional equation in 3 variables in the quasi-Banach space

Abstract

In this paper, we investigate the Ulam type stability for the $3$-dimensional quadratic functional equation $$g(a +b+c)+g(a-b)+g(a-c)+g(b-c)=3[g(a) + g(b)+g(c)]$$ in the setting of quasi-Banach space using the Brzdęk fixed point approach. The results obtained in this paper extend various previously known results in the setting of quasi-Banach space. We also give some examples to illustrate our main results.