UNICITY OF MEROMORPHIC FUNCTION WITH THEIR SHIFT OPERATOR SHARING SMALL FUNCTION

In this paper, we introduce a new notation of reduced linear shift operator $ L_{c}^{r}(\phi) $, and with the aid of this new operator, we study the uniqueness of meromorphic functions $ \phi(z) $ and $ L_{c}^{r}(\phi) $ share $ \infty $ CM in the extended complex plane. The results obtained in the paper significantly improve a existing result. Further, using the notion of sets, we deal the same problem. We exhibit a handful result to justify certain statements relevant to the content of the paper.