Document Type : Research Paper

Authors

• S. Zolfaghari ¹
• A. Ebadian ¹
• S. Ostadbashi ¹
• M. De La Sen ²
• M. Eshaghi Gordji ³

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 $k\ne 0,\pm 1.$

Keywords

• Hyers-Ulam stability
• AQ functional Equation
• Fixed point
• Probabilistic Modular Space