NEVANLINNA'S FIVE-VALUE THEOREM FOR DERIVATIVE'S OF MEROMORPHIC FUNCTIONS PARTIALLY SHARING VALUES ON ANNULI
RENUKADEVI S. DYAVANAL *
Department of Mathematics, Karnatak University, Dharwad-580003, India
ASHOK RATHOD
Department of Mathematics, Karnatak University, Dharwad-580003, India
*Author to whom correspondence should be addressed.
Abstract
In this paper, we first obtain Xiong Inequality of meromorphic function on annuli. Next by using this inequality, we generalise Nevanlinnas five-value theorem for derivatives of meromorphic functions by considering weaker assumptions of sharing five-values to partially sharing k(≥ 5) values. As a particular case of our results, we deduce several results.
Keywords: Nevanlinna theory, the annuli