See manuscript PDF for complete Abstract:
In this paper, we apply some special functions to introduce a new class of control functions which help us define the concept of multi-stability. Further, we investigate the multi-stability of homomorphisms in C*-algebras and Lie C*-algebras and multi-stability of derivations in C*-algebras and Lie C*-algebras for the following random operator equation via fixed point methods:\[ \mu f(\eth, \frac{x+y}{2}) + \mu f(\eth,\frac{x-y}{2}) = f(\eth ,\mu x) .\]
In particular for $\mu = 1$, the above equation turns out to be Jensen's random operator equation.