  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 and Harina - Anand not only by sharing small function
instead of fixed point but also reducing the lower bound of $ n $. The authors
Harina-Anand made plenty of mistakes in their paper. 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.
