Throughout this work,we explore the uniqueness properties of meromorphic functions concerning their interactions with complex differential-difference polynomial.Under the condition of finite order,we establish three d...Throughout this work,we explore the uniqueness properties of meromorphic functions concerning their interactions with complex differential-difference polynomial.Under the condition of finite order,we establish three distinct uniqueness results for a meromorphic function f associated with the differential-difference polynomial L_(η)^(n)f=Σ_(k=0)^(n)a_(k)f (z+k_(η))+a_(-1)f′.These results lead to a refined characterization of f (z)≡L_(η)^(n)f (z).Several illustrative examples are provided to demonstrate the sharpness and precision of the results obtained in this study.展开更多
In this paper we deal with the problem of uniqueness of meromorphic functions with two deficient values and obtain a result which is an improvement of that of F. Gross and Yi Hougxun.
In this article, we study the uniqueness question of nonconstant meromorphic functions whose nonlinear differential polynomials share 1 or have the same fixed points in an angular domain. The results in this article i...In this article, we study the uniqueness question of nonconstant meromorphic functions whose nonlinear differential polynomials share 1 or have the same fixed points in an angular domain. The results in this article improve Theorem 1 of Yang and Hua [26], and improve Theorem 1 of Fang and Qiu [6].展开更多
This paper investigate the uniqueness problems for meromorphic functions that share three values CM and proves a uniqueness theorem on this topic which can be used to improve some previous related results.
In this paper,we investigate two meromorphic functions which share small functions dealing with multiple values.By constructing auxiliary functions,especially by the deep analysis of counting functions we obtain some ...In this paper,we investigate two meromorphic functions which share small functions dealing with multiple values.By constructing auxiliary functions,especially by the deep analysis of counting functions we obtain some results which extend the existing results of some scholars.展开更多
The uniqueness of meromorphic functions with one sharing value and an equality on deficiency is studied. We show that if two nonconstant meromorphic functions f(z) and g(z) satisfy δ(0,f)+δ(0,g)+δ(∞,f)+δ(∞,g)=3 ...The uniqueness of meromorphic functions with one sharing value and an equality on deficiency is studied. We show that if two nonconstant meromorphic functions f(z) and g(z) satisfy δ(0,f)+δ(0,g)+δ(∞,f)+δ(∞,g)=3 or δ 2(0,f)+δ 2(0,g)+δ 2(∞,f)+δ 2(∞,g)=3, and E(1,f)=E(1,g) then f(z),g(z) must be one of five cases.展开更多
In this paper, the uniqueness problems on meromorphic function f(z) of zero order sharing values with their q-shift f(qz + c) are studied. It is shown that if f(z) and f(qz + c) share one values CM and IM respectively...In this paper, the uniqueness problems on meromorphic function f(z) of zero order sharing values with their q-shift f(qz + c) are studied. It is shown that if f(z) and f(qz + c) share one values CM and IM respectively, or share four values partially, then they are identical under an appropriate deficiency assumption.展开更多
In this paper, we shall study the uniqueness problems of meromorphic functions of differential polynomials sharing two values IM. Our results improve or generalize many previous results on value sharing of meromorphic...In this paper, we shall study the uniqueness problems of meromorphic functions of differential polynomials sharing two values IM. Our results improve or generalize many previous results on value sharing of meromorphic functions.展开更多
In this paper we study the uniqueness of certain meromorphic functions. It is shown that any two nonconstant meromorphic functions of order less than one, that share four values IM or six values SCM, must be identical...In this paper we study the uniqueness of certain meromorphic functions. It is shown that any two nonconstant meromorphic functions of order less than one, that share four values IM or six values SCM, must be identical. As a consequence, a result due to W. W. Adams and E. G. Straus is generalized.展开更多
In this paper, we first obtain the famous Xiong Inequality of meromorphic functions on annuli. Next we get a uniqueness theorem of meromorphic function on annuli concerning to their multiple values and derivatives by ...In this paper, we first obtain the famous Xiong Inequality of meromorphic functions on annuli. Next we get a uniqueness theorem of meromorphic function on annuli concerning to their multiple values and derivatives by using the inequality.展开更多
We prove an oscillation theorem of two meromorphic functions whose derivatives share four values IM. From this we obtain some uniqueness theorems, which improve the corresponding results given by Yang [16] and Qiu [10...We prove an oscillation theorem of two meromorphic functions whose derivatives share four values IM. From this we obtain some uniqueness theorems, which improve the corresponding results given by Yang [16] and Qiu [10], and supplement results given by Nevanlinna [9] and Gundersen [3, 4]. Some examples are provided to show that the results in this paper are best possible.展开更多
In this paper, by using the idea of truncated counting functions of meromorphic functions, we deal with the problem of uniqueness of the meromorphic functions whose certain nonlinear differential polynomials share one...In this paper, by using the idea of truncated counting functions of meromorphic functions, we deal with the problem of uniqueness of the meromorphic functions whose certain nonlinear differential polynomials share one finite nonzero value.展开更多
Let E(a;f) be the set of a-points of a meromorphic function f(z) counting multiplicities. We prove that if a transcendental meromorphic function f(z) of hyper order strictly less than 1 and its nth exact difference Δ...Let E(a;f) be the set of a-points of a meromorphic function f(z) counting multiplicities. We prove that if a transcendental meromorphic function f(z) of hyper order strictly less than 1 and its nth exact difference Δnc f(z) satisfy E(1;f)= E(1;Δnc f), E(0;f) E(0;Δnc f) and E(1;f) E(1;Δnc f), then Δnc f(z) f(z). This result improves a more recent theorem due to Gao et al.(Gao Z, Kornonen R, Zhang J, Zhang Y. Uniqueness of meromorphic functions sharing values with their nth order exact differences. Analysis Math., 2018, https://doi.org/10.1007/s10476- 018-0605-2) by using a simple method.展开更多
In this paper, we prove a result on the uniqueness of meromorphic functions sharing three values counting multiplicity and improve a result obtained by Xiaomin Li and Hongxun Yi.
Considering the uniqueness of meromorphic functions concerning differential monomials ,we obtain that, if two non-constant meromorphic functions f(z) and g(z) satisfy ,where k and n are tow positive integers satisfyin...Considering the uniqueness of meromorphic functions concerning differential monomials ,we obtain that, if two non-constant meromorphic functions f(z) and g(z) satisfy ,where k and n are tow positive integers satisfying k ≥ 3 and n ≥ 11 , then either where c1, c2, c, are three constants, satisfying (c1 c2)n+1c>n+1=- 1 or f = tg for a constant t such that tn+1 =展开更多
Aim To study the value distribution of meromorphic functions in angular domains, the deficiency, the deficient value, the Nevanlinna direction and other singular directions. Methods A fundamental inequality of Nevan...Aim To study the value distribution of meromorphic functions in angular domains, the deficiency, the deficient value, the Nevanlinna direction and other singular directions. Methods A fundamental inequality of Nevanlinna characteristic functions in the angular domain was used, which is similar with the Nevanlinna secondary fundamental theorem. Results The deficiency and deficient value of meromorphic functions about an angular domain and a direction were defined. The definition of Nevanlinna direction was improved. Conclusion For a family of meromorphic functions, it is proved that the number of deficient values is at most countable and the sum of deficiencies isnt greater than 2. The existence of the Nevanlinna direction is obtained. The existence of Borel and Julia directions and the relation between them are found.展开更多
In this paper, we consider the problem of the uniqueness for meromorphic functions whose n-th derivatives share the same 1-points. The results in this paper are different from all of theorems given by H X Yi and C C Y...In this paper, we consider the problem of the uniqueness for meromorphic functions whose n-th derivatives share the same 1-points. The results in this paper are different from all of theorems given by H X Yi and C C Yang and other authors.展开更多
In this paper, we study the value distribution question of certain difference polynomials of meromorphic functions, and investigate the uniqueness questions of meromorphic functions whose certain difference polynomial...In this paper, we study the value distribution question of certain difference polynomials of meromorphic functions, and investigate the uniqueness questions of meromorphic functions whose certain difference polynomials share a small functions. The results in this paper improve and extend the corresponding results in Zhang [16] and Chen [1].展开更多
基金Supported by the National Natural Science Foundation of China (Grant No.12161074)the Talent Introduction Research Foundation of Suqian University (Grant No.106-CK00042/028)+1 种基金Suqian Sci&Tech Program (Grant No.M202206)Sponsored by Qing Lan Project of Jiangsu Province and Suqian Talent Xiongying Plan of Suqian。
文摘Throughout this work,we explore the uniqueness properties of meromorphic functions concerning their interactions with complex differential-difference polynomial.Under the condition of finite order,we establish three distinct uniqueness results for a meromorphic function f associated with the differential-difference polynomial L_(η)^(n)f=Σ_(k=0)^(n)a_(k)f (z+k_(η))+a_(-1)f′.These results lead to a refined characterization of f (z)≡L_(η)^(n)f (z).Several illustrative examples are provided to demonstrate the sharpness and precision of the results obtained in this study.
文摘In this paper we deal with the problem of uniqueness of meromorphic functions with two deficient values and obtain a result which is an improvement of that of F. Gross and Yi Hougxun.
基金supported by the NSFC(11171184)the NSF of Shandong Province,China(Z2008A01)
文摘In this article, we study the uniqueness question of nonconstant meromorphic functions whose nonlinear differential polynomials share 1 or have the same fixed points in an angular domain. The results in this article improve Theorem 1 of Yang and Hua [26], and improve Theorem 1 of Fang and Qiu [6].
基金Supported by the NSF of China(10371065)Supported by the NSF of Zhejiang Province (M103006)
文摘This paper investigate the uniqueness problems for meromorphic functions that share three values CM and proves a uniqueness theorem on this topic which can be used to improve some previous related results.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11871108,11571362)Teacher Research Capacity Promotion Program of Beijing Normal University Zhuhai,Guangdong Natural Science Foundation(Grant No.2018A030313954)+1 种基金Guangdong University(New Generation Information Technology)Key Field Project(Grant No.2020ZDZX3019)Project of Guangdong Province Innovative Team(Grant No.2020WCXTD011).
文摘In this paper,we investigate two meromorphic functions which share small functions dealing with multiple values.By constructing auxiliary functions,especially by the deep analysis of counting functions we obtain some results which extend the existing results of some scholars.
文摘The uniqueness of meromorphic functions with one sharing value and an equality on deficiency is studied. We show that if two nonconstant meromorphic functions f(z) and g(z) satisfy δ(0,f)+δ(0,g)+δ(∞,f)+δ(∞,g)=3 or δ 2(0,f)+δ 2(0,g)+δ 2(∞,f)+δ 2(∞,g)=3, and E(1,f)=E(1,g) then f(z),g(z) must be one of five cases.
基金Supported by the National Natural Science Foundation of China(11661044)
文摘In this paper, the uniqueness problems on meromorphic function f(z) of zero order sharing values with their q-shift f(qz + c) are studied. It is shown that if f(z) and f(qz + c) share one values CM and IM respectively, or share four values partially, then they are identical under an appropriate deficiency assumption.
文摘In this paper, we shall study the uniqueness problems of meromorphic functions of differential polynomials sharing two values IM. Our results improve or generalize many previous results on value sharing of meromorphic functions.
文摘In this paper we study the uniqueness of certain meromorphic functions. It is shown that any two nonconstant meromorphic functions of order less than one, that share four values IM or six values SCM, must be identical. As a consequence, a result due to W. W. Adams and E. G. Straus is generalized.
基金Supported by the National Natural Science Foundation of China(Grant No.11126327)the Natural Science Foundation of Guangdong Province(Nos.2016A030313002+1 种基金2015A030313644)the Training Plan for the Outstanding Young Teachers in Higher Education of Guangdong Province(Grant No.Yq2013159)
文摘In this paper, we first obtain the famous Xiong Inequality of meromorphic functions on annuli. Next we get a uniqueness theorem of meromorphic function on annuli concerning to their multiple values and derivatives by using the inequality.
基金supported by the NSFC (11171184), the NSFC(10771121),the NSFC (40776006) the NSFC & RFBR (Joint Project) (10911120056),the NSF of Shandong Province, China (Z2008A01), and the NSF of Shandong Province, China (ZR2009AM008)
文摘We prove an oscillation theorem of two meromorphic functions whose derivatives share four values IM. From this we obtain some uniqueness theorems, which improve the corresponding results given by Yang [16] and Qiu [10], and supplement results given by Nevanlinna [9] and Gundersen [3, 4]. Some examples are provided to show that the results in this paper are best possible.
基金The NSF(11301076)of Chinathe NSF(2014J01004)of Fujian Province
文摘In this paper, by using the idea of truncated counting functions of meromorphic functions, we deal with the problem of uniqueness of the meromorphic functions whose certain nonlinear differential polynomials share one finite nonzero value.
基金The NSF (11801291) of China,the NSF (2018J01424) of Fujian Province
文摘Let E(a;f) be the set of a-points of a meromorphic function f(z) counting multiplicities. We prove that if a transcendental meromorphic function f(z) of hyper order strictly less than 1 and its nth exact difference Δnc f(z) satisfy E(1;f)= E(1;Δnc f), E(0;f) E(0;Δnc f) and E(1;f) E(1;Δnc f), then Δnc f(z) f(z). This result improves a more recent theorem due to Gao et al.(Gao Z, Kornonen R, Zhang J, Zhang Y. Uniqueness of meromorphic functions sharing values with their nth order exact differences. Analysis Math., 2018, https://doi.org/10.1007/s10476- 018-0605-2) by using a simple method.
文摘In this paper, we prove a result on the uniqueness of meromorphic functions sharing three values counting multiplicity and improve a result obtained by Xiaomin Li and Hongxun Yi.
文摘Considering the uniqueness of meromorphic functions concerning differential monomials ,we obtain that, if two non-constant meromorphic functions f(z) and g(z) satisfy ,where k and n are tow positive integers satisfying k ≥ 3 and n ≥ 11 , then either where c1, c2, c, are three constants, satisfying (c1 c2)n+1c>n+1=- 1 or f = tg for a constant t such that tn+1 =
文摘Aim To study the value distribution of meromorphic functions in angular domains, the deficiency, the deficient value, the Nevanlinna direction and other singular directions. Methods A fundamental inequality of Nevanlinna characteristic functions in the angular domain was used, which is similar with the Nevanlinna secondary fundamental theorem. Results The deficiency and deficient value of meromorphic functions about an angular domain and a direction were defined. The definition of Nevanlinna direction was improved. Conclusion For a family of meromorphic functions, it is proved that the number of deficient values is at most countable and the sum of deficiencies isnt greater than 2. The existence of the Nevanlinna direction is obtained. The existence of Borel and Julia directions and the relation between them are found.
基金Foundation item: Supported by the NSF of China(10471028)Supported by the NSF of Guangdong Province(020586) Supported by the Guangzhou Education Bureau(2006, 2025)Supported by the Grant-in-Aid for Scientific Research 2004(15540151)Supported by the Japan Society for the Promotion of Science
文摘In this paper, we consider the problem of the uniqueness for meromorphic functions whose n-th derivatives share the same 1-points. The results in this paper are different from all of theorems given by H X Yi and C C Yang and other authors.
基金funded by the National Natural Science Foundation of China(project No.11171184)
文摘In this paper, we study the value distribution question of certain difference polynomials of meromorphic functions, and investigate the uniqueness questions of meromorphic functions whose certain difference polynomials share a small functions. The results in this paper improve and extend the corresponding results in Zhang [16] and Chen [1].
