Fixed point theory for multi-valued operators via admissible perturbation approach

Source abstract

In this paper, we will consider the following problem: if a fixed point inclusion x ∈ B(x) (where B is a ”bad” multi-valued operator) is replaced by another fixed point inclusion x ∈ G(x) (where G is now a ”good/better” multi-valued operator), then which properties (existence, data dependence, stability) can be obtained for our initial problem in terms of some conditions on the new operator G? We will do this by the help of the admissible perturbation technique, which will generate a “good” multi-operator G related to the ”bad” multi-valued operator B by the fact that the fixed point set of B and respectively of G coincide.