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

Document Type : Research Paper

Authors

1 Department of Mathematics, Urmia University, Urmia, Iran

2 Institute of Research and Development of Processes University of Basque Country Campus of Leioa (Bizkaia) - Aptdo. 644- Bilbao, 48080- Bilbao, Spain

3 Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, Semnan 35195-363, Iran

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 $k\neq 0,\pm1.$

Keywords