Some properties of meromorphic solutions of higher order linear difference equations

Belaïdi, Benharrat; Benkarouba, Yamina

doi:10.5937/spsunp1902075x

Cited by 6 publications

(18 citation statements)

References 14 publications

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“…Therefore, Theorems 5-9 are found to reduce to some known corresponding results. For example, In addition, it may be interesting to compare Theorem 10 and (Reference [15], Theorem 10).…”

Section: Resultsmentioning

confidence: 99%

“…Here, and in the following, let ϕ : [0, ∞) → (0, ∞) be a non-decreasing unbounded function. [13,[15][16][17][18][19]). The ϕ-order and the ϕ-lower order of a meromorphic function f are defined, respectively, as…”

Section: Remark 1 (Referencementioning

confidence: 99%

“…For a later use, from the Equation 1, we find that, for f ( ≡ 0 Then, some easily-derivable implications among measure, logarithmic measure, upper density, and upper logarithmic density are given in the following remark. [15], Proposition 1). Let E ⊂ [1, ∞).…”

Section: Introductionmentioning

confidence: 96%

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Growth Analysis of Meromorphic Solutions of Linear Difference Equations with Entire or Meromorphic Coefficients of Finite φ-Order

Choi

Datta

Biswas³

2021

Symmetry

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Many researchers’ attentions have been attracted to various growth properties of meromorphic solution f (of finite φ-order) of the following higher order linear difference equation Anzfz+n+...+A1zfz+1+A0zfz=0, where Anz,…,A0z are entire or meromorphic coefficients (of finite φ-order) in the complex plane (φ:[0,∞)→(0,∞) is a non-decreasing unbounded function). In this paper, by introducing a constant b (depending on φ) defined by lim̲r→∞logrlogφ(r)=b<∞, and we show how nicely diverse known results for the meromorphic solution f of finite φ-order of the above difference equation can be modified.

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“…Therefore, Theorems 5-9 are found to reduce to some known corresponding results. For example, In addition, it may be interesting to compare Theorem 10 and (Reference [15], Theorem 10).…”

Section: Resultsmentioning

confidence: 99%

Section: Remark 1 (Referencementioning

confidence: 99%

See 1 more Smart Citation

Growth Analysis of Meromorphic Solutions of Linear Difference Equations with Entire or Meromorphic Coefficients of Finite φ-Order

Choi

Datta

Biswas³

2021

Symmetry

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“…In this paper, a meromorphic function means a function that is meromorphic in the whole complex plane C. Throughout this paper, we assume that the reader is familiar with the fundamental results and the standard notations of the Nevanlinna theory of meromorphic functions [4,7,19]. Recently, many articles focused on complex difference equations [1,10,[13][14][15]20,21]. The background for these studies lies in the recent difference counterparts of Nevanlinna theory.…”

Section: Introduction and Statement Of Main Resultsmentioning

confidence: 99%

“…Remark 1.16 Theorem 1.13 is the improvement of Theorems 1.8-1.9 and Theorem 1.14 is the improvement of Theorem 1.10. Furthermore, Theorem 1.15 is the improvement of Theorem 1.5 [21] and Theorem 1.4 [1].…”

Section: Introduction and Statement Of Main Resultsmentioning

confidence: 99%

Study of the growth properties of meromorphic solutions of higher-order linear difference equations

Belaïdi

Bellaama

2021

Arab. J. Math.

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In this paper, we investigate the growth of meromorphic solutions of homogeneous and non-homogeneous linear difference equations $$\begin{aligned} A_{k}(z)f(z+c_{k})+\cdots +A_{1}(z)f(z+c_{1})+A_{0}(z)f(z)= & {} 0, \\ A_{k}(z)f(z+c_{k})+\cdots +A_{1}(z)f(z+c_{1})+A_{0}(z)f(z)= & {} F, \end{aligned}$$ A k ( z ) f ( z + c k ) + ⋯ + A 1 ( z ) f ( z + c 1 ) + A 0 ( z ) f ( z ) = 0 , A k ( z ) f ( z + c k ) + ⋯ + A 1 ( z ) f ( z + c 1 ) + A 0 ( z ) f ( z ) = F , where $$A_{k}\left( z\right) ,\ldots ,A_{0}\left( z\right) ,$$ A k z , … , A 0 z , $$F\left( z\right) $$ F z are meromorphic functions and $$c_{j}$$ c j $$\left( 1,\ldots ,k\right) $$ 1 , … , k are non-zero distinct complex numbers. Under some conditions on the coefficients, we extend early results due to Zhou and Zheng, Belaïdi and Benkarouba.

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Growth properties of meromorphic solutions of some higher-order linear differential-difference equations

Bellaama

Belaïdi

2022

Analysis

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This paper is devoted to the study of the growth of meromorphic solutions of homogeneous and non-homogeneous linear differential-difference equations ∑ i = 0 n ∑ j = 0 m A i ⁢ j ⁢ f ( j ) ⁢ ( z + c i ) = 0 , \displaystyle\sum_{i=0}^{n}\sum_{j=0}^{m}A_{ij}f^{(j)}(z+c_{i})=0, ∑ i = 0 n ∑ j = 0 m A i ⁢ j ⁢ f ( j ) ⁢ ( z + c i ) = F , \displaystyle\sum_{i=0}^{n}\sum_{j=0}^{m}A_{ij}f^{(j)}(z+c_{i})=F, where A i ⁢ j {A_{ij}} ( i = 0 , … , n {i=0,\ldots,n} , j = 0 , … , m {j=0,\ldots,m} ), F are meromorphic functions and c i {c_{i}} ( 0 , … , n {0,\ldots,n} ) are non-zero distinct complex numbers. Under some conditions on the coefficients, we extend early results due to Zhou and Zheng.

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Some properties of meromorphic solutions of higher order linear difference equations

Abstract: In this paper, we investigate the growth of solutions of the linear difference equations

Cited by 6 publications

References 14 publications

Growth Analysis of Meromorphic Solutions of Linear Difference Equations with Entire or Meromorphic Coefficients of Finite φ-Order

Growth Analysis of Meromorphic Solutions of Linear Difference Equations with Entire or Meromorphic Coefficients of Finite φ-Order

Study of the growth properties of meromorphic solutions of higher-order linear difference equations

Growth properties of meromorphic solutions of some higher-order linear differential-difference equations

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