Fixed points for multivalued contractions with respect to a Pompeiu type metric

The purpose of this paper is to present a fixed point theory for multivalued H+-contractions from the following perspectives: existence/uniqueness of the fixed and strict fixed points, data dependence of the fixed point set, sequence of multivalued operators and fixed points, Ulam-Hyers stability of a multivalued fixed point equation, well-posedness of the fixed point problem, limit shadowing property for a multivalued operator, set-to-set operatorial equations and fractal operator theory.