C ∗ $C^{*}$ -Algebra valued fuzzy normed spaces with application of Hyers–Ulam stability of a random integral equation

Abstract

Abstract In this paper, we consider C ∗ $C^{*}$ -algebra valued fuzzy normed spaces. We study the random integral equation ( 1 2 c ) ∫ x − c d x + c d u ( γ , τ , d 0 ) d τ = u ( γ , x , d ) $(\frac{1}{2c})\int _{x-cd}^{x+cd}u(\gamma ,\tau ,d_{0})\,d\tau =u( \gamma ,x,d)$ which is related to the stochastic wave equation. In addition, using a C ∗ $C^{*}$ -algebra valued fuzzy controller function, we consider its C ∗ $C^{*}$ -algebra valued fuzzy Hyers–Ulam stability.

Keywords

• Nonlinear random integral equation
• Stochastic wave equation
• Iterative method
• Random operator
• Fuzzy normed space
• C ∗ $C^{*}$ -algebra valued fuzzy set