This research is a continuation of a recent paper due to the first four authors. Shared value problems related to a meromorphic function f (z) and its shift f (z + c), where c ∈ C, are studied. It is shown, for instance, that if f (z) is of finite order and shares two values CM and one value IM with its shift f (z + c), then f is a periodic function with period c. The assumption on the order of f can be dropped if f shares two shifts in different directions, leading to a new way of characterizing elliptic functions. The research findings also include an analogue for shifts of a well-known conjecture by Brück concerning the value sharing of an entire function f with its derivative f .
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.