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_r^r(ϕ), and with the aid of this new operator, we study the uniqueness of meromorphic functions ϕ(z) and L_r^r(ϕ) share ∞ 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. [ABSTRACT FROM AUTHOR]