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

Document Type: Research Paper

Authors

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Abstract

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

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