Sharkovskii's theorem for connectivity Gδ-relations

A version of Sharkovskii's cycle coexistence theorem is formulated for a composition of connectivity G(delta)-relations with closed values. Thus, a multivalued version in [Andres & Pastor, 2005] holding with at most two exceptions for M-maps, jointly with a single-valued version in [Szuca, 2003], for functions with a connectivity G(delta)-graph, are generalized. In particular, our statement is applicable to differential inclusions as well as to some discontinuous functions.