Bulletin of the
Korean Mathematical Society BKMS

In this paper, we have studied on the uniqueness problems of meromorphic functions with its linear $c$-shift operator in the light of partial sharing. Our two results improve and generalize two very recent results of Noulorvang-Pham [Bull. Korean Math. Soc. 57 (2020), no. 5, 1083--1094] in some sense. In addition, our other results have improved and generalized a series of results due to L\"u-L\"u [Comput. Methods Funct. Theo. 17 (2017), no. 3, 395--403], Zhen [J. Contemp. Math. Anal. 54 (2019), no. 5, 296--301] and Banerjee-Bhattacharyya [Adv. Differ. Equ. 509 (2019), 1--23]. We have exhibited a number of examples to show that some conditions used in our results are essential.

Keywords: Meromorphic function, uniqueness, linear $c$-shift operator, partial sharing, small function

MSC numbers: Primary 32A22; Secondary 30D35

Supported by: The second author is thankful to Council of Scienti c and Industrial Research (India) for their financial support under File No: 09/106(0191)/2019-EMR-I.