Iterative Fixed Point Techniques in Generalized Ulam Stability

Constructive fixed point theorems are useful tools in arguing for Ulam-type stability for many equations. In this work we change the perspective. First we give some results regarding the stability of the fixed points equation—results which are themselves constructive fixed point theorems that generalize some known criteria. We then use iterative techniques and results obtained for the fixed point equation to demonstrate the stability of a broad classes of equations. Finally, we give an example of the use of the obtained results in the homomorphisms equation by providing classes of control functions that ensure its generalized stability.