Acta mathematica scientia, Series B >
ON UNIQUENESS OF MEROMORPHIC FUNCTIONS WITH SHARED-SETS IN AN ANGULAR DOMAIN
Online published: 2011-01-20
In this article, we deal with the uniqueness problems on meromorphic functions sharing two finite sets in an angular domain instead of the whole plane C. In particular, we investigate the uniqueness for meromorphic functions of infinite order in an angular domain and obtain some results. Moreover, examples show that the conditions in theorems are necessary.
Key words： Shared-set; uniqueness; meromorphic function; angular domain; infinite order
CHEN Sheng-Jiang , LIN Wei-Chuan . ON UNIQUENESS OF MEROMORPHIC FUNCTIONS WITH SHARED-SETS IN AN ANGULAR DOMAIN[J]. Acta mathematica scientia, Series B, 2011 , 31(1) : 194 -206 . DOI: 10.1016/S0252-9602(11)60220-8
[1] Baernsein A. Proof of Edrei's spread conjecture. Proc London Math Soc, 1973, 26: 418--434
[2] Chuang C T. Sur les fonctions-types. Sci Sinica, 1961, 10: 171--181
[3] Edrei A. Sums of deiciencies of meromorphic functions. J Analyse Math, 1965, 14: 79--107
[4] Gol'dberg A A. Nevanlinna's lemma on the logarithmic derivative of meromorphic function. Mat Zametki, 1975, 17: 525--529
[5] Gol'dberg A A, Ostroskii I V. The distribution of values of meromorphic functions//Moscow: Izdat. Nauka, 1970, Value distribution of meromorphic functions. Translations of Mathematical Monographs 236, AMS, 2008
[6] Hayman W K. Meromorphic Functions. Oxford: Claredon Press, 1964.
[7] Hiong K L . Sur les fonctions entières et les fonctions m\'{e}romprhes d'order infini. J de Math, 1935, 14: 233--308
[8] Lin W , Mori S , Tohge K. Uniqueness theorems in an angular domain. Tohoku Math J, 2006, 58: 509--527
[9] Nevanlinna R. Uber die Eigenschaften meromorpher Funktionen in einem Winkelraum. Acta Soc Sci Fenn, 1925, 50: 1--45
[10] Wu Z J , Sun D C. On angular distribution in complex oscillation. Acta Math Sin, Chinese series, 2007, 50: 1297--1304
[11] Yang L. Borel direction of meromorphic functions in an angular domain. Sci Sinica, Special Issue I on Math , 1979.
[12] Yi H X, Yang C C. Uniqueness Theory of Meromorphic Functions. Beijing: Sci Press, 1995
[13] Yi H X , Lin W. Uniqueness of meromorphic functions and a question of Gross. Kyunggpook Math J, 2006, 46: 437--444
[14] Zheng J H. On uniqueness of meromorphic functions with four shared values in one angular domain. Complex Var Theory Appl, 2003,
48: 777--786
[15] Zheng J H. On uniqueness of meromorphic functions with shared values in some angular domains. Canad Math Bull, 2004, 47: 152--160
[16] Zheng J H. On transcendental meromorphic functions with radially distributed values. Sci China Ser A, 2004, 47: 401--416
[17] Zhang Q C. Meromorphic functions sharing values in an angular domain. J Math Anal Appl, 2009, 349: 100--112
/
| 〈 |
|
〉 |