A new proof of a unicity theorem of meromorphic functions and their derivatives

The purpose of this article is twofold. The first is to prove a unicity theorem for meromorphic functions sharing five small functions regardless of multiplicities. This is an improvement of the results of Yahua–Jianyong, Yao and Yi, Thai and Tan. The second is to prove a finiteness theorem for meromorphic functions that share three small functions ignoring multiplicity and another small function with multiplicities truncated by 2.

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MEROMORPHIC FUNCTIONS SHARING SMALL FUNCTIONS AS TARGETS

International Journal of Mathematics ◽

10.1142/s0129167x0500293x ◽

2005 ◽

Vol 16 (04) ◽

pp. 437-451 ◽

Cited By ~ 10

Author(s):

DO DUC THAI ◽

TRAN VAN TAN

Keyword(s):

Meromorphic Functions ◽

Unicity Theorem ◽

Remarkable Improvement ◽

Small Functions

The purpose of this article is twofold. The first is to prove the unicity theorem with truncated multiplicities of meromorphic functions sharing five small functions. This gives a remarkable improvement of the results of Yuhua–Jianyong, Yao and Yi. The second is to generalize the unicity theorem of Fujimoto to meromorphic functions sharing four small functions with truncated multiplicities.

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An extension of unicity theorem for meromorphic functions

Tohoku Mathematical Journal ◽

10.2748/tmj/1178225843 ◽

1993 ◽

Vol 45 (4) ◽

pp. 491-497 ◽

Cited By ~ 5

Author(s):

Manabu Shirosaki

Keyword(s):

Meromorphic Functions ◽

Unicity Theorem

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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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