Study of Uniqueness of Meromorphic Functions with the Difference Operator

There are some uniqueness problems with meromorphic functions with difference operators that we looked into in this paper. We looked at them in the light of partial sharing. Specifically, we have obtained two uniqueness results by considering sharing and partial sharing of small functions. In the first theorem and shares CM, whereas in the second theorem and partially share CM. 2010 AMS Classification: 30D35, 30D45 Keywords and phrases: Uniqueness, Meromorphic function, Difference operator, Small function, Partial sharing.