Meromorphic function sharing a small function with a linear differential polynomial

Characteristic function of a meromorphic function and its derivatives

In this paper, some results of Singh, Gopalakrishna and Kulkarni (1970s) have been extended to higher order derivatives. It has been shown that, if $sumlimits_{a}Theta(a, f)=2$ holds for a meromorphic function $f(z)$ of finite order, then for any positive integer $k,$ $T(r, f)sim T(r, f^{(k)}), rrightarrowinfty$ if $Theta(infty, f)=1$ and $T(r, f)sim (k+1)T(r, f^{(k)}), rrightarrowinfty$ if $Th...

Nonlinear Differential Polynomials Sharing a Small Function

Dealing with a question of Lahiri [6] we study the uniqueness problem of meromorphic functions concerning two nonlinear differential polynomials sharing a small function. Our results will not only improve and supplement the results of Lin-Yi [16], Lahiri Sarkar [12] but also improve and supplement a very recent result of the first author [1].

Weighted sharing of a small function by a meromorphic function and its derivative

In this paper, we study the relationship between a meromorphic function and its k-th order derivative which share a small function with weight(multiplicities) l(a positive integer)ignoring multiplicity. MR(2010) Subject Classification: 30D35.

Uniqueness of Transcendental Meromorphic Functions with Their Nonlinear Differential Polynomials Sharing the Small Function

Uniqueness and Differential Polynomials of Meromorphic Functions Sharing a Polynomial

In this paper, we deal with the uniqueness problems of meromorphic functions when certain nonlinear differential polynomials generated by them share a nonconstant polynomial counting multiplicities by considering that the functions share in nity, ignoring multiplicities. The research ndings also include IM-analogues of the theorem in which the nonconstant polynomial is allowed to be shared igno...