Strict fixed point and stability results for multivalued operators via the admissible perturbation technique

We consider a class of multi-valued operators T:X→ P(X) having the property that there exists an admissible perturbation of it, defined as TG:X→ P(X) and satisfying a Ćirić type contraction condition. This work focuses on the conditions imposed on the admissible perturbation TG , such that strict fixed point results hold true for T. The main result consists of formulating a theorem that connects the properties of the admissible perturbation with the conclusion that T is a Picard operator. Additionally, we study whether the strict fixed point problem T(x)=\ is well-posed, as well as, data dependence, Ulam-Hyers stability and Ostrowski property for the strict fixed point problem. The admissible perturbations in the sense of Takahashi serve as a relevant example for applying the theory formulated in this paper.