Special functions and multi-stability of the Jensen type random operator equation in C*-algebras via fixed point

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

Automated summary

In this paper, new control functions are defined using special functions, introducing the concept of multi-stability. The multi-stability of homomorphisms in C*-algebras and Lie C*-algebras, as well as the multi-stability of derivations in C*-algebras, are investigated. The random operator equation is analyzed using fixed point methods, with a particular focus on Jensen's random operator equation when mu=1.