Communications of the
Korean Mathematical Society CKMS

In this paper, we prove a uniqueness theorem of non-constant meromorphic functions of hyper-order less than $1$ sharing two values CM and two partial shared values IM with their shifts. Our result in this paper improves and extends the corresponding results from Chen-Lin \cite{CL2016}, Charak-Korhonen-Kumar \cite{CKK2016}, Heittokangas-Korhonen-Laine-Rieppo-Zhang \cite{HKLRZ2009} and Li-Yi \cite{LY2016}. Some examples are provided to show that some assumptions of the main result of the paper are necessary.

Keywords: Meromorphic function, Nevanlinna theory, uniqueness, partially sharing values

MSC numbers: Primary 30D35

Supported by: This work was financially supported by UGC India (F.16-6(DEC.2016)/2017(NET)).