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Uniqueness of certain polynomials of meromorphic functions sharing a set with finite weight

Abstract

We investigated the Brück type conjecture and generalized the existing result by extending them up to a difference-differential polynomial \(\mathcal{P}[\xi]\) sharing a small function with a certain differential polynomial \(\mathcal{L}[\xi]\) of a meromorphic function. The class of all meromorphic solutions of the differential equation \(\mathcal{P}[\xi] \equiv \mathcal{L}[\xi]\) has been explored. Our result will generalize and extend the result due to A. Banerjee and B. Chakraborty [3]. For the generalization of our main result, some relevant questions have finally been posed for further study in this direction.

2020 Mathematics Subject Classification:

30D35

Keywords

uniqueness, meromorphic functions, difference-differential polynomial, differential polynomial, weighted sharing, set sharing

Full text

Author Details

Harina P. Waghamore

Department of Mathematics
Jnanabharathi Campus
Bangalore University
Bengaluru-560056, India
e-mails: harina@bub.ernet.in, harinapw@gmail.com

B. N. Naveenkumar

Department of Mathematics
Jnanabharathi Campus
Bangalore University
Bengaluru-560056, India
emails: bnk_maths@bub.ernet.in, nknateshmaths1@gmail.com


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