Singular Direction and q-Difference Operator of Meromorphic Functions

2020 ◽  
Vol 43 (5) ◽  
pp. 3693-3709
Author(s):  
Jianren Long ◽  
Jianyong Qiao ◽  
Xiao Yao
Keyword(s):  
Meromorphic Functions ◽  
Difference Operator ◽  
Singular Direction

scholarly journals Fixed Points of Difference Operator of Meromorphic Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-4
Author(s):  
Zhaojun Wu ◽  
Hongyan Xu
Keyword(s):  
Meromorphic Function ◽  
Fixed Points ◽  
Meromorphic Functions ◽  
Difference Operator ◽  
Transcendental Meromorphic Function ◽  
Exact Difference ◽  
Borel Exceptional Values ◽  
Nevanlinna Deficiency

Letfbe a transcendental meromorphic function of order less than one. The authors prove that the exact differenceΔf=fz+1-fzhas infinitely many fixed points, ifa∈ℂand∞are Borel exceptional values (or Nevanlinna deficiency values) off. These results extend the related results obtained by Chen and Shon.

Value distribution for nth difference operator of meromorphic functions with maximal deficiency sum

2018 ◽  
Vol 27 (3) ◽  
pp. 797-811 ◽  
Author(s):  
Subhas S. Bhoosnurmath ◽  
Renukadevi S. Dyavanal ◽  
Mahesh Barki ◽  
Ashok Rathod
Keyword(s):  
Meromorphic Functions ◽  
Difference Operator ◽  
Value Distribution ◽  
Maximal Deficiency

scholarly journals On a new singular direction of meromorphic functions

2004 ◽  
Vol 69 (2) ◽  
pp. 277-287 ◽  
Author(s):  
Guo Hui ◽  
Zheng Jian Hua ◽  
Tuen Wai Ng
Keyword(s):  
Characteristic Function ◽  
Meromorphic Functions ◽  
Comparison Function ◽  
Nevanlinna Characteristic ◽  
Singular Direction

In this paper, by using Ahlfors' theory of covering surfaces, we establish the existence of a new singular direction for a meromorphic functions f, namely a T direction for f, for which the Nevanlinna characteristic function T(r, f) is used as a comparison function.

scholarly journals Certain q-difference operators and their applications to the subclass of meromorphic q-starlike functions

Filomat ◽  
2019 ◽  
Vol 33 (11) ◽  
pp. 3385-3397 ◽  
Author(s):  
Qazi Ahmad ◽  
Nazar Khan ◽  
Mohsan Raza ◽  
Muhammad Tahir ◽  
Bilal Khan
Keyword(s):  
Differential Operator ◽  
Meromorphic Functions ◽  
Difference Operator ◽  
Starlike Functions ◽  
Difference Operators ◽  
Sufficient Condition ◽  
Coefficient Inequalities ◽  
Meromorphic Starlike Functions

The main aim of this work is to find some coefficient inequalities and sufficient condition for some subclasses of meromorphic starlike functions by using q-difference operator. Here we also define the extended Ruscheweyh differential operator for meromorphic functions by using q-difference operator. Several properties such as coefficient inequalities and Fekete-Szego functional of a family of functions are investigated.

MEROMORPHIC FUNCTIONS SHARE TWO VALUES WITH ITS DIFFERENCE OPERATOR

2014 ◽  
Vol 0 (0) ◽  
Author(s):  
Yeyang Jiang ◽  
Zongxuan Chen
Keyword(s):  
Meromorphic Functions ◽  
Difference Operator ◽  
Uniqueness Problem ◽  
Morphic Function

Abstract In this paper, we investigate the uniqueness problem related to a mero- morphic function f(z) and its difference operator Δf(z) = f(z + n) - f(z), and we prove that Δf(z) and f(z) share a,b CM, where f(z) is a meromorpnic function with N(r,f) = S(r,f), then f(z + η) = 2f(z).

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