scholarly journals Uniqueness of Functions with Its Shifts or Difference Operators

2018 ◽  
Author(s):  
Rajshree Dhar
Keyword(s):  
Meromorphic Function ◽  
Finite Order ◽  
Difference Operator ◽  
Difference Operators

It is shown that if a non-constant meromorphic function f(z) is of finite order and shares certain values with its shifts/difference operators then f(z) coincides with that particular shift/difference operator.

scholarly journals Uniqueness Problems about Entire Functions with Their Difference Operator Sharing Sets

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Fan Niu ◽  
Jianming Qi ◽  
Zhiyong Zhou
Keyword(s):  
Finite Order ◽  
Difference Operator ◽  
Entire Functions ◽  
Difference Operators ◽  
Transcendental Entire Functions

In this paper, we study the uniqueness questions of finite order transcendental entire functions and their difference operators sharing a set consisting of two distinct entire functions of finite smaller order. Our results in this paper improve the corresponding results from Liu (2009) and Li (2012).

Orlicz lacunary sequence spaces of 𝑙-fractional difference operators

2020 ◽  
Vol 26 (2) ◽  
pp. 173-183
Author(s):  
Kuldip Raj ◽  
Kavita Saini ◽  
Anu Choudhary
Keyword(s):  
Difference Operator ◽  
Lacunary Sequence ◽  
Sequence Spaces ◽  
Difference Operators ◽  
Normed Spaces ◽  
Fractional Difference ◽  
New Approach ◽  
Inclusion Relations ◽  
Difference Sequence Spaces ◽  
Bounded Sequences

AbstractRecently, S. K. Mahato and P. D. Srivastava [A class of sequence spaces defined by 𝑙-fractional difference operator, preprint 2018, http://arxiv.org/abs/1806.10383] studied 𝑙-fractional difference sequence spaces. In this article, we intend to make a new approach to introduce and study some lambda 𝑙-fractional convergent, lambda 𝑙-fractional null and lambda 𝑙-fractional bounded sequences over 𝑛-normed spaces. Various algebraic and topological properties of these newly formed sequence spaces have been explored, and some inclusion relations concerning these spaces are also established. Finally, some characterizations of the newly formed sequence spaces are given.

scholarly journals On Properties of Differences Polynomials about Meromorphic Functions

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
Jianming Qi ◽  
Jie Ding ◽  
Wenjun Yuan
Keyword(s):  
Meromorphic Function ◽  
Finite Order ◽  
Special Class ◽  
Meromorphic Functions ◽  
Value Distribution ◽  
Class Difference ◽  
Difference Polynomial

We study the value distribution of a special class difference polynomial about finite order meromorphic function. Our methods of the proof are also different from ones in the previous results by Chen (2011), Liu and Laine (2010), and Liu and Yang (2009).

scholarly journals Value distribution of meromorphic functions concerning rational functions and differences

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Mingliang Fang ◽  
Degui Yang ◽  
Dan Liu
Keyword(s):  
Positive Integer ◽  
Meromorphic Function ◽  
Rational Function ◽  
Finite Order ◽  
Meromorphic Functions ◽  
Rational Functions ◽  
Value Distribution ◽  
Exponent Of Convergence ◽  
Nonzero Constant ◽  
Zero Points

AbstractLet c be a nonzero constant and n a positive integer, let f be a transcendental meromorphic function of finite order, and let R be a nonconstant rational function. Under some conditions, we study the relationships between the exponent of convergence of zero points of $f-R$ f − R , its shift $f(z+nc)$ f ( z + n c ) and the differences $\Delta _{c}^{n} f$ Δ c n f .

scholarly journals Logarithmic derivative estimates of meromorphic functions of finite order in the half-plane

2020 ◽  
Vol 54 (2) ◽  
pp. 172-187
Author(s):  
I.E. Chyzhykov ◽  
A.Z. Mokhon'ko
Keyword(s):  
Meromorphic Function ◽  
Finite Order ◽  
Half Plane ◽  
Meromorphic Functions ◽  
Logarithmic Derivative ◽  
Sharp Estimates ◽  
Exceptional Sets ◽  
Upper Half Plane ◽  
Logarithmic Derivatives

We established new sharp estimates outside exceptional sets for of the logarithmic derivatives $\frac{d^ {k} \log f(z)}{dz^k}$ and its generalization $\frac{f^{(k)}(z)}{f^{(j)}(z)}$, where $f$ is a meromorphic function $f$ in the upper half-plane, $k>j\ge0$ are integers. These estimates improve known estimates due to the second author in the class of meromorphic functions of finite order.Examples show that size of exceptional sets are best possible in some sense.

scholarly journals On the singularities of the inverse to a meromorphic function of finite order

1995 ◽  
pp. 355-373 ◽  
Author(s):  
Walter Bergweiler ◽  
Alexandre Eremenko
Keyword(s):  
Meromorphic Function ◽  
Finite Order

scholarly journals A note on a result of Singh and Kulkarni

2000 ◽  
Vol 23 (4) ◽  
pp. 285-288 ◽  
Author(s):  
Mingliang Fang
Keyword(s):  
Meromorphic Function ◽  
Finite Order ◽  
Transcendental Meromorphic Function

We prove that iffis a transcendental meromorphic function of finite order and∑a≠∞δ(a,f)+δ(∞,f)=2, thenK(f(k))=2k(1−δ(∞,f))1+k−kδ(∞,f), whereK(f(k))=limr→∞N(r,1/f(k))+N(r,f(k))T(r,f(k))This result improves a result by Singh and Kulkarni.

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.

Difference Operators in Simulation Data Warehouses

2017 ◽  
Vol 12 (2) ◽  
pp. 347-354 ◽  
Author(s):  
Jing Zhao ◽  
◽  
Yoshiharu Ishikawa ◽  
Yukiko Wakita ◽  
Kento Sugiura
Keyword(s):  
Difference Operator ◽  
Difference Operators ◽  
Observation Data ◽  
Temporal Data ◽  
Data Warehouses ◽  
Simulation Data ◽  
Tsunami Disaster ◽  
Spatio Temporal ◽  
The Difference ◽  
Mass Evacuation

In analyzing observation data and simulation results, there are frequent demands for comparing more than one data on the same subject to detect any differences between them. For example, comparison of observation data for an object in a certain spatial domain at different times or comparison of spatial simulation data with different parameters. Therefore, this paper proposes the difference operator in spatio-temporal data warehouses, which store temporal and spatial observation data and simulation data. The requirements for the difference operator are summarized, and the approaches to implement them are presented. In addition, the proposed approach is applied to the mass evacuation of simulation data in a tsunami disaster, and its effectiveness is verified. Extensions of the difference operator and their applications are also discussed.

Sign in / Sign up

Export Citation Format

Share Document