본문 바로가기
KERD
논문KCI 등재

Unicity of mermorphic functions concerning shared functions with their difference

Dan Liu|Mingliang Fang|Bingmao Deng
대한수학회 (The Korean Mathematical Society)|2019.11|대한수학회보 (Bulletin of the KMS)|제56권 제6호|pp. 1511-1524|DOI 10.4134/BKMS.b181222

1

조회

0

다운로드

0

인용

0

참고문헌

키워드

uniquenessmeromorphic functionsdifference operators
주제분류수학

초록

In this paper, we investigate the uniqueness of meromorphic functions of finite order concerning sharing small functions and prove that if $f(z)$ and $\Delta_c f(z)$ share $a(z), b(z), \infty$ CM, where $a(z), b(z) (\not \equiv \infty)$ are two distinct small functions of $f(z)$, then $f(z)\equiv \Delta_cf(z)$. The result improves the results due to Li et al.~(\cite{LXM}), Cui et al.~(\cite{CN}) and L\"{u} et al.~(\cite{LF}).

Abstract

In this paper, we investigate the uniqueness of meromorphic functions of finite order concerning sharing small functions and prove that if $f(z)$ and $\Delta_c f(z)$ share $a(z), b(z), \infty$ CM, where $a(z), b(z) (\not \equiv \infty)$ are two distinct small functions of $f(z)$, then $f(z)\equiv \Delta_cf(z)$. The result improves the results due to Li et al.~(\cite{LXM}), Cui et al.~(\cite{CN}) and L\"{u} et al.~(\cite{LF}).

참고문헌 (17)

  1. Ning Cui, "The conjecture on unity of meromorphic functions concerning their differences", Journal of Difference Equations and Applications, 22(10), pp.1452~1471 (2016), Informa UK Limited[DOI]
  2. B. Q. Chen, "Uniqueness theorems on entire functions and their dierence operators or shifts", Abstr. Appl. Anal, 2012, pp.8~ (2012)[DOI]
  3. Zong-Xuan Chen, "On Sharing Values of Meromorphic Functions and Their Differences", Results in Mathematics, 63(1-2), pp.557~565 (2013), Springer Science and Business Media LLC[DOI]
  4. Yik-Man Chiang, "On the Nevanlinna characteristic of f(z+η) and difference equations in the complex plane", The Ramanujan Journal, 16(1), pp.105~129 (2008), Springer Science and Business Media LLC[DOI]
  5. R.G. Halburd, "Difference analogue of the Lemma on the Logarithmic Derivative with applications to difference equations", Journal of Mathematical Analysis and Applications, 314(2), pp.477~487 (2006), Elsevier BV[DOI]
  6. R. G. Halburd, "Nevanlinna theory for the dierence operator", Ann. Acad. Sci. Fenn. Math, 31(2), pp.463~478 (2006)
  7. W. K. Hayman, "Meromorphic Functions, Oxford Mathematical Monographs" (1964), Clarendon Press
  8. J. Heittokangas, "Value sharing results for shifts of meromorphic functions, and sufficient conditions for periodicity", Journal of Mathematical Analysis and Applications, 355(1), pp.352~363 (2009), Elsevier BV[DOI]
  9. Xiao-Min Li, "RESULTS ON MEROMORPHIC FUNCTIONS SHARING THREE VALUES WITH THEIR DIFFERENCE OPERATORS", 대한수학회보, 52(5), pp.1401~1422 (2015), 대한수학회
  10. Yuhua Li, "The uniqueness of meromorphic functions concerning small functions", Science in China Series A: Mathematics, 43(6), pp.581~590 (2000), Springer Science and Business Media LLC[DOI]
  11. D. Liu, "Unicity of entire functions concerning shifts and dierence operators", Abstr. Appl. Anal, 2014, pp.5~ (2014)[DOI]
  12. Feng Lü, "Meromorphic Functions Sharing Three Values with their Difference Operators", Computational Methods and Function Theory, 17(3), pp.395~403 (2017), Springer Science and Business Media LLC[DOI]
  13. R. Nevanlinna, "Le theoreme de Picard-Borel et la theorie des fonctions meromorphes" (1974), Chelsea Publishing Co.
  14. Chung-Chun Yang, "On deficiencies of differential polynomials, II", Mathematische Zeitschrift, 125(2), pp.107~112 (1972), Springer Science and Business Media LLC[DOI]
  15. C.-C. Yang, "Uniqueness Theory of Meromorphic Functions" (2003), Kluwer Academic Publishers Group
  16. L. Yang, "Value Distribution Theory" (1993), Springer-Verlag
  17. Jie Zhang, "Entire functions sharing some values with their difference operators", Science China Mathematics, 57(10), pp.2143~2152 (2014), Springer Science and Business Media LLC[DOI]

관련 논문AI추천

Uniqueness theorem for a meromorphic function and its exact differenceAizhu Xu, Shengjiang Chen대한수학회 · 대한수학회보2020 · 제57권 제5호Meromorphic Function Sharing Two Small Functions with Its DerivativeKai Liu, Xiao-guang Qi경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2009 · 제49권 제2호UNIQUENESS RESULTS ON MEROMORPHIC FUNCTIONS AND THEIR DIFFERENCE OPERATORS SHARING TARGETS WITH WEIGHTDuc Thoan Pham, Hong Nhat Nguyen, Thu Thuy Hoang대한수학회 · 대한수학회보2023 · 제60권 제2호Some results on uniqueness of meromorphic solutions of difference equationsXiao Ming Wang, Zong Sheng Gao대한수학회 · 대한수학회논문집2017 · 제32권 제4호Meromorphic functions sharing four values with their difference operators or shiftsHong-Xun Yi, Xiao-Min Li대한수학회 · 대한수학회보2016 · 제53권 제4호Uniqueness of Meromorphic Functions Concerning the Difference PolynomialsFanghong Liu, Hong-Xun Yi경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2015 · 제55권 제2호

이 간행물의 다른 논문 (17건)

Extension of phase-isometries between the unit spheres of atomic $L_p$-spaces for $p>0$Xujian Huang, Xihong Jinpp. 1377-1384Negacyclic codes of length $8p^s$ over $\mathbb{F}_{p^m}+u\mathbb{F}_{p^m}$Jirayu Phuto, Chakkrid Klin-eampp. 1385-1422Riemann-Liouville fractional fundamental theorem of calculus and Riemann-Liouville fractional Polya type integral inequality and its extension to Choquet integral settingGeorge A. Anastassioupp. 1423-1433Reliability analysis of checkpointing model with multiple verification mechanism이유태pp. 1435-1445Mild solutions for the relativistic Vlasov-Klein-Gordon systemXianwen Zhang, Meixia Xiaopp. 1447-1465
원문 보기