2021/08/17 by Molla Basir Ahamed, Ahamed, Molla Basir
Mathematics · #30D35 #Advanced Differential Equations and Dynamical Systems #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Meromorphic and Entire Functions
paper · pdf · doi:10.48550/arxiv.2108.07562
openalex publication_date 2021/08/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Two meromorphic functions f and g are said to share a value s∈ℂ∪\∞\ CM (IM) provided that f(z)-s and g(z)-s have the same set of zeros counting multiplicities (ignoring multiplicities). We say that a meromorphic function f share s∈ℂ partially CM with a meromorphic function g if E(s,f)⊆ E(s,g). It is easy to see that the condition ``partially shared values CM " is more general than the condition ``shared value CM ". With the idea of partially shared values, in this paper, we prove some uniqueness results between non-constant meromorphic functions and their shifts or generalized differences. We exhibit some examples to show that the result of Charak et al. \citeCha & Kor & Kum-2016 is not true for k=2 or k=3 . We find some gaps in proof of the result of Lin et al. \citeLin & Lin & Wu, and we not only correct them but also generalize their result in a more convenient way. A number of examples have been exhibited to validate a certain claim of the main results of this paper and also to show that some of the conditions are sharp. In the end, we have posed some open questions for further investigation of the main result of the paper.