Abstract
In the paper, we have investigated on a conjecture posed by Chen and Yi (Results Math 63:557–565, 2013) concerning the uniqueness problem of meromorphic functions f sharing three distinct values with their difference $${\mathcal {L}}_c(f) $$ . We have proved the conjecture for finite ordered meromorphic functions. Some examples have been exhibited in the paper to show that the main result is true also for the meromorphic function of infinite order, but we are unable to prove our results for the function of infinite order, and hence we conjecture it. The main results in the paper also generalized a result of Zhang and Liao (Sci China Math 57(10):2143–2152, 2014). This research also shows that when a meromorphi function f satisfies a certain relation of the type $$ {\mathcal {L}}_c(f)\equiv f $$ , then it can be found the class of all such functions.
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