A power of a combination of meromorphic function with its shift sharing small function with its derivative

Abstract

In this paper, we use the idea of normal family to investigate the situation when a power of a combination of transcendental meromorphic function with its shift shares small function with it's derivative and obtain three results which improve and generalize the recent result due to Lu and Yi [12]. Also we exhibit some examples to fortify the condition of our results.

Mathematics Subject Classication (2010): Primary: 30D35; Secondary: 30D30.

Key words: Meromorphic functions, derivative, Nevanlinna theory, normal family.