On a generalization of a result of Zhang and Yang

Abstract

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