A fixed point approach to the Hyers-Ulam stability of an $AQ$ functional equation in probabilistic modular spaces

Abstract

In this paper, we prove the Hyers-Ulam stability in<br />$beta$-homogeneous probabilistic modular spaces via fixed point method for the functional equation<br />[<br />f(x+ky)+f(x-ky)=f(x+y)+f(x-y)+frac{2(k+1)}{k}f(ky)-2(k+1)f(y)<br />]<br />for fixed integers $k$ with $kneq 0,pm1.$