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

نویسندگان
Zolfaghari, S. ID 1
Ebadian, A. ID 2
Ostadbashi, S. ID 3
De La Sen, M. ID 4
Eshaghi Gordji, M. ID 5

1 Department of Mathematics, Urmia University, Urmia, Iran

2 Department of Mathematics, Urmia University, Urmia, Iran

3 Department of Mathematics, Urmia University, Urmia, Iran

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

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

doi
10.22075/ijnaa.2013.60
چکیده

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 $k\neq 0,\pm1.$

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