With the help of the notion of weighted sharing of sets, in this paper we have investigated on the question posed by Yi [17] regarding the uniqueness of meromorphic functions concerning three set sharing and obtained a result which significantly improved the recent results of Banerjee - Ahamed [3], Banerjee - Mukherjee [5] and Banerjee - Majumder [4] by removing the extra supposition as well as relaxing the nature of sharing. We have exhibited some examples to show the sharpness of the cardinalities of the set S 1 and the set S 2 considered in 1.1 and also to show that one can not obtained the same conclusions of the main results by considering any arbitrary sets.
AbstractWe prove some uniqueness theorems concerning the derivatives of meromorphic functions when they share two or three sets which will improve some existing results.
Taking the question posed by the first author in [1] into background, we
further exhaust-ably investigate existing Fujimoto type Strong Uniqueness
Polynomial for Meromorphic functions (SUPM). We also introduce a new kind of
SUPM named Restricted SUPM and exhibit some results which will give us a new
direction to discuss the characteristics of a SUPM. Moreover, throughout the
paper, we pose a number of open questions for future research.
On uniqueness of two meromorphic functions when sharing three sets with finite weights
