On uniqueness of two meromorphic functions sharing three sets with finite weights

2020/05/02 by Molla Basir Ahamed, Ahamed, Molla Basir
Mathematics · #30d35 #Complex Variables (math.CV) #FOS: Mathematics #Meromorphic and Entire Functions #math.CV #msc:30d35

paper · pdf · doi:10.48550/arxiv.2005.05780

arxiv created 2020/05/02 · openalex publication_date 2020/05/02 · arxiv updated 2020/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

With the help of the notion of weighted sharing of sets, this paper dealt with the question posed by Yi \citeYi-SC-1994 regarding the uniqueness of meromorphic functions concerning three set sharing. A result has been proved which significantly improved the recent results of Banerjee - Ahamed [Bull. Polish Acad. Sci., 62(3)(2014), 243--256.], \Banerjee - Mukherjee [Hokkaido Math. J., 37(2008), 507--530.] and Banerjee - Majumder [Analysis, 34(2)(2014), 143--162.] by relaxing the nature of sharing. Several examples have been exhibited to show the sharpness of the cardinalities of the sets S₁ and S₂ considered in Theorem 1.1. Moreover, we give some constructive examples to endorse the validity of our established theorem.

Related

• Two and three shared sets uniqueness problem on restricted and unrestricted ordered meromorphic functions
• Uniqueness of meromorphic functions that share Two Sets
• Uniqueness of a meromorphic function and its linear difference polynomial sharing two sets with finite weight
• Uniqueness and two shared set problems of L-Function and certain class of meromorphic function
• Further Investigations on Weighted Value Sharing and Uniqueness of Meromorphic Functions