meromorphic functions

In this paper, we study the uniqueness of meromorphic functions with q-shift difference-differential polynomials $F=P(f)\prod\limits_{j=1}^{d}f(q_{j}z+c_{j})^{v_{j}}]^{(k)}$ and $G=[P(g)\prod\limits_{j=1}^{d}g(q_{j}z+c_{j})^{v_{j}}]^{(k)}$, where $P(z)$ is a non-constant polynomial with degree $n$ sharing a finite value. The results of this paper are an extension of the previous theorems given by Harina P. Waghamore and Rajeshwari S [19].

The study of the Nevanlinna theory for difference operators was introduced independently by Halburd & Korhonen and Chiang & Feng in the years 2006 and 2008 respectively. Halburd and Korhonen proved the uniqueness theorem for meromorphic functions associated with c-separated pairs. In this paper, we have generalised the result by introducing c-separated pairs of multiplicity p and their counting functions. We have deduced some analogues of certain unique results of classical Nevanlinna theory due to Chen, Chen & Tsai; Gopalakrishna & Bhoosnurmath; and Lahiri & Pal. Thereafter, we have also discussed certain implications of the deduced results.

In this paper, we investigate an interesting subclass of univalent functions. Also, we introduce a new subclass of meromorphic bi-univalent functions. We obtain the estimates on the initial Taylor-Maclurin Coefficients for functions in the interesting subclass of meromorphically bi-univalent functions defined on Δ={z∈C: 1<|z|<∞}Δ={z∈C: 1<|z|<∞}.

In this research we stated and proved the some escape criteria theorems of the one parameter family of the transcendental meromorphic-functions F={fk(z)=k csc(z):k∈C and\ z∈C}. Furthermore, we used non-standard iterations: Mann, Ishikawa and Noor iterations in the complex plane. This research can be considered as an extension of [1].

In this paper, we introduce a new operator Ωc g(z) associated with polylogarithm function, applying it on the subclasses AHΣ∗ B (γ, k) of meromorphic starlike bi-univalent functions of order γ, and AHΣe∗ B (γ, k) of meromorphic strongly starlike bi-univalent functions of order γ, also we find estimates on the coefficients |b0| and |b1| for functions in these subclasses.

Using the techniques of the differential subordination and superordination, we derive certain subordination and superordination properties of multivalent functions associated with the Dziok-Srivastava operator.

Let 𝝨 be the class of meromorphic bi-univalent functions f of the formf(z)=z+b_0+∑_(n=1)^∞▒b_n/z^n ,which are univalent (analytic and one to one) on the domain Δ={z∈C∶1

In this paper, we consider a new class of analytic functions in the unit disk using polynomials of order alpha. We give some sufficient conditions for functions belonging to this class.

In this paper, we introduce new classes ∑ k,p,n (α,m,λ,l,ρ) and T k,p,n (α,m,λ,l,ρ) of p valent meromorphic functions defined by using the extended multiplier transformation operator. We use a strong convolution technique and derive inclusion results. A radius problem and some other interesting properties of these classes are discussed.

In this article, we consider the uniqueness of the difference monomials f n (z)f(z+c). Suppose that f(z) and g(z) are transcendental meromorphic functions with finite order and E k (1,f n (z)f(z+c))=E k (1,g n (z)g(z+c)). Then we prove that if one of the following holds (i) n≥14 and k≥3, (ii) n≥16 and k=2, (iii) n≥22 and k=1, then f(z)≡t 1 g(z) or f(z)g(z)=t 2, for some constants t 1 and t 2 that satisfy t n+1 1 =1 and t n+1 2 =1. We generalize some previous results of Qi et. al.

In this paper, we defined two classes S ∗ p (n,λ,A,B) and\\ K p (n,λ,A,B) of meromorphic p− valent functions associated with a new linear operator. We obtained convolution properties for functions in these classes.