On a generalization of a result of Zhang and Yang

Abhijit Banerjee, Sujoy Majumder

In this paper we find out the specific form of a meromorphic function when a generalized linear expression of the function share a small function with its $k$-th derivative counterpart. Our result will improve and generalize a few existing results, especially that of Zhang and Yang [J. L. Zhang and L. Z. Yang, A power of a meromorphic function sharing a small function with its derivative, Ann. Acad. Sci. Fenn. Math., 34 (2009), 249-260].