On Uniqueness of Two Meromorphic Functions Sharing A Small Function

Abstract

In this paper, we have investigated the uniqueness problems of entire and meromorphic functions concerning differential polynomials sharing a small function. Our results radically extended and improved the results of Bhoosnurmath-Pujari [6] and Harina - Anand [13] not only by sharing small function instead of fixed point but also reducing the lower bound of $ n $. There are some miscalculation in the proof of a result of Harina-Anand [13]. We have corrected all of them in a more convenient way. At last some open questions have been posed for further study in this direction.