Weighted set sharing and uniqueness of meromorphic functions

Pulak Sahoo; Samar Halder

doi:10.5486/pmd.2021.8933

Weighted set sharing and uniqueness of meromorphic functions

Publicationes Mathematicae Debrecen ◽

10.5486/pmd.2021.8933 ◽

2021 ◽

Vol 99 (3-4) ◽

pp. 371-388

Author(s):

Pulak Sahoo ◽

Samar Halder

Keyword(s):

Meromorphic Functions ◽

Set Sharing

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

Matematychni Studii ◽

10.30970/ms.53.2.147-158 ◽

2020 ◽

Vol 53 (2) ◽

pp. 147-158

Author(s):

M. B. Ahamed

Keyword(s):

Meromorphic Functions ◽

Weighted Sharing ◽

Set Sharing

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.

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Uniqueness and set sharing of derivatives of meromorphic functions

Mathematica Slovaca ◽

10.2478/s12175-011-0005-6 ◽

2011 ◽

Vol 61 (2) ◽

Cited By ~ 2

Author(s):

Abhijit Banerjee ◽

Pranab Bhattacharjee

Keyword(s):

Meromorphic Functions ◽

Uniqueness Theorems ◽

Set Sharing ◽

Derivatives Of

AbstractWe prove some uniqueness theorems concerning the derivatives of meromorphic functions when they share two or three sets which will improve some existing results.

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Further investigations on Fujimoto type strong uniqueness polynomials

Filomat ◽

10.2298/fil1716203b ◽

2017 ◽

Vol 31 (16) ◽

pp. 5203-5216

Author(s):

Abhijit Banerjee ◽

Bikash Chakraborty ◽

Sanjay Mallick

Keyword(s):

Meromorphic Functions ◽

Future Research ◽

Strong Uniqueness ◽

Open Questions

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.

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