Meromorphic Functions Sharing Pairs of Small Functions
-
Jilong Zhang
and
Lianzhong Yang
Abstract
In this paper, we investigate the relations between two meromorphic functions that share some pairs of small functions. In particular, we show that two meromorphic functions that share six pairs of small functions IM∗ must be linked by quasi-Möbius transformation. We also give some properties of two meromorphic functions sharing five pairs of values or small functions.
References
[1] CZUBIAK, T. P.-GUNDERSEN, G. G.: Meromorphic functions that share pairs of values, Complex Variables 34 (1997), 35-46.Search in Google Scholar
[2] GUNDERSEN, G. G.: Meromorphic functions that share three or four values, J. Lond. Math. Soc. (2) 20 (1979), 457-466.10.1112/jlms/s2-20.3.457Search in Google Scholar
[3] GUNDERSEN, G. G.: Meromorphic functions that share five pairs of values, Complex Var. Elliptic Equ. 56 (2011), 93-99.10.1080/17476930903394937Search in Google Scholar
[4] HAYMAN, W. K.: Meromorphic Functions, Clarendon Press, Oxford, 1964.Search in Google Scholar
[5] HU, P. C.-LI, P.-YANG, C. C.: Unicity of Meromorphic Mappings, Kluwer Academic Publishers, Dordrecht-Boston-London, 2003.10.1007/978-1-4757-3775-2Search in Google Scholar
[6] ISHIZAKI, K.: Meromorphic functions sharing small functions, Arch. Math. (Basel) 77 (2011), 273-277.10.1007/PL00000491Search in Google Scholar
[7] LAINE, I.: Nevanlinna Theory and Complex Differential Equations, Walter de Gruyter, Berlin-New York, 1993.10.1515/9783110863147Search in Google Scholar
[8] LI, B. Q.: Uniqueness of entire functions sharing four small functions, Amer. J. Math. 119 (1997), 841-858.10.1353/ajm.1997.0025Search in Google Scholar
[9] LI, P.: Meromorphic functions that share four small functions, J. Math. Anal. Appl. 263 (2001), 316-326.10.1006/jmaa.2001.7607Search in Google Scholar
[10] LI, Y. H.-QIAO, J. Y.: The uniqueness of Meromorphic functions concerning small functions, Adv. Math. (China) 28 (1999), 87-88.Search in Google Scholar
[11] NEVANLINNA, R.: Le théorème de Picard-Borel et la théorie des fonctions meromorphes, Gauthiers-Villars, Paris, 1929.10.1007/BF02592680Search in Google Scholar
[12] REINDERS, M.: A new characterization of Gundersen’s example of two meromorphic functions sharing four values, Results Math. 24 (1993), 174-179.10.1007/BF03322327Search in Google Scholar
[13] YANG, C. C.-YI, H. X.: Uniqueness Theory of Meromorphic Functions, Kluwer Academic Publishers, Dordrecht, 2003. 10.1007/978-94-017-3626-8Search in Google Scholar
© 2015 Mathematical Institute Slovak Academy of Sciences
Articles in the same Issue
- The M-Regular Graph of a Commutative Ring
- Further Properties of the Lattice of Torsion Classes of Abelian Cyclically Ordered Groups
- Free Power-Commutative Groupoids
- On Systems of Independent Sets
- Note on G-Module Structure of Orders
- Semisimple Hopf Algebras of Dimension 2q3
- On the Convergence of a Mapped by a Function
- Multiple Solutions of Nonlinear Fractional Differential Equations with p-Laplacian Operator and Nonlinear Boundary Conditions
- Meromorphic Functions Sharing Pairs of Small Functions
- Sharp Inequalities for Polygamma Functions
- Existence Results for Some Higher-Order Evolution Equations with Time-Dependent Unbounded Operator Coefficients
- Existence of Ground State Solutions for Hamiltonian Elliptic Systems with Gradient Terms
- Approximate Higher Ring Derivations in Non-Archimedean Banach Algebras
- Characterizations of Banach Spaces which are not Isomorphic to any of their Proper Subspaces
- Operator Inequalities Related to Q-Class Functions
- On a Class of Locally Dually Flat (α,β)–Metrics
- Limit Theorems for the Counting Function of Eigenvalues up to Edge in Covariance Matrices
- A Generalization of Jakubec's Formula
Articles in the same Issue
- The M-Regular Graph of a Commutative Ring
- Further Properties of the Lattice of Torsion Classes of Abelian Cyclically Ordered Groups
- Free Power-Commutative Groupoids
- On Systems of Independent Sets
- Note on G-Module Structure of Orders
- Semisimple Hopf Algebras of Dimension 2q3
- On the Convergence of a Mapped by a Function
- Multiple Solutions of Nonlinear Fractional Differential Equations with p-Laplacian Operator and Nonlinear Boundary Conditions
- Meromorphic Functions Sharing Pairs of Small Functions
- Sharp Inequalities for Polygamma Functions
- Existence Results for Some Higher-Order Evolution Equations with Time-Dependent Unbounded Operator Coefficients
- Existence of Ground State Solutions for Hamiltonian Elliptic Systems with Gradient Terms
- Approximate Higher Ring Derivations in Non-Archimedean Banach Algebras
- Characterizations of Banach Spaces which are not Isomorphic to any of their Proper Subspaces
- Operator Inequalities Related to Q-Class Functions
- On a Class of Locally Dually Flat (α,β)–Metrics
- Limit Theorems for the Counting Function of Eigenvalues up to Edge in Covariance Matrices
- A Generalization of Jakubec's Formula
