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Uniqueness of meromorphic functions of differential polynomials sharing a small function with finite weight

Waghamore Harina P., Bhoosnurmath Vijaylaxmi

Journal of Applied Analysis

2019

Vol. 25, nr 2

141--153

Let f be a non-constantmeromorphic function and a = a(z) (≢ 0,∞) a small function of f . Here, we obtain results similar to the results due to Indrajit Lahiri and Bipul Pal [Uniqueness of meromorphic functions with their homogeneous and linear differential polynomials sharing a small function, Bull. KoreanMath. Soc. 54 (2017), no. 3, 825-838] for a more general differential polynomial by introducing the concept ofweighted sharing.

Defective functions of meromorphic functions in the unit disc

Ciechanowicz E.

Journal of Applied Analysis

2016

Vol. 22, nr 1

15--26

Let f be a meromorphic function in the unit disc and (aν)kν=1 a set of distinct meromorphic functions small with respect to f. An analogue of the second main theorem for f and (aν)kν=1 is given. Upper limits for the sum of defects of an admissible meromorphic function and an admissible holomorphic function follow. For meromorphic and holomorphic functions in the unit disc and their small functions the analogues of Ullrich's theorem are presented.

On an open problem of Xiao-Bin Zhang and Jun-Feng Xu

Majumder S.

Demonstratio Mathematica

2016

Vol. 49, nr 2

161--182

The purpose of the paper is to study the uniqueness of meromorphic functions sharing a nonzero polynomial. The results of the paper improve and generalize the recent results due to X. B. Zhang and J. F. Xu [19]. We also solve an open problem as posed in the last section of [19].