The Multivalued Fibre Contraction Principle and Applications

Abstract In this paper, we will extend the Fibre Contraction Principle (FCP) to the case of multivalued operators. Starting with an extended variant of the Multivalued Contraction Principle, a Multivalued Fibre Contraction Principle will be proved. The special case of multivalued operators having strict fixed points and some open questions for the case of nonself operators are also presented. Some applications to a triangular system of integral inclusions and to multivalued fibre fractals are also given.