Sets and value sharing of q-differences of meromorphic functions
1
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
In this paper, we investigate uniqueness problems of certain types of q-difference polynomials, which improve some results in [20]. However, our proof is different from that in [20]. Moreover, we obtain a uniqueness result in the case where q-differences of two entire functions share values as well. This research also shows that there exist two sets, such that for a zero-order non-constant meromorphic function f and a non-zero complex constant q, E(Sj , f) = E(Sj ,△qf) for j = 1, 2 imply f(z) = t△qf, where tn = 1. This gives a partial answer to a question of Gross concerning a zero order meromorphic function f(z) and △qf.
Abstract
In this paper, we investigate uniqueness problems of certain types of q-difference polynomials, which improve some results in [20]. However, our proof is different from that in [20]. Moreover, we obtain a uniqueness result in the case where q-differences of two entire functions share values as well. This research also shows that there exist two sets, such that for a zero-order non-constant meromorphic function f and a non-zero complex constant q, E(Sj , f) = E(Sj ,△qf) for j = 1, 2 imply f(z) = t△qf, where tn = 1. This gives a partial answer to a question of Gross concerning a zero order meromorphic function f(z) and △qf.
참고문헌 (20)
- D. C. Barnett, "Nevanlinna theory for the q-difference operator and meromorphic solutions of q-difference equations", Proc. Roy. Soc. Edinburgh Sect. A, 137(3), pp.457~474 (2007)
- G. Frank, "A unique range set for meromorphic functions with 11 elements", Complex Var. Theory Appl, 37(1), pp.185~193 (1998)
- F. Gross, "Factorization of meromorphic functions and some open problems", Proc. Conf., Univ. Kentucky, 599, pp.51~67 (1977)
- F. Gross, "Entire functions with common preimages, in: Factorization theory of meromorphic functions and related topics, In Lecture Notes in Pure and Appl. Math., 78", pp.19~24, Dekker
- X. H. Hua, "A unicity theorem for entire functions", Bull. London Math. Soc, 22(5), pp.457~462 (1990)
- I. Laine, "Clunie theorem for difference and q-difference polynomials", J. London. Math. Soc, 76(3), pp.556~566 (2007)
- R. Nevanlinna, "Le theoreme de Picard-Borel et la theorie des fonctions meromorphes" (1929), Gauthiers-Villars
- Xiaoguang Qi, "Value sharing results of a meromorphic function f(z) and f(qz)", 대한수학회보, 48(6), pp.1235~1243 (2011), 대한수학회
- X. G. Qi, "Share sets of q-difference of meromorphic functions", Math. Slovaca
- K. Shibazaki, "Unicity theorem for entire functions of finite order", Mem. Nat. Defense Acad, 21(3), pp.67~71 (1981)
- C. C. Yang, "On two entire functions which together with their first derivative have the same zeros", J. Math. Anal. Appl, 56(1), pp.1~6 (1976)
- C. C. Yang, "Uniqueness Theory of Meromorphic Functions" (2003), Kluwer Academic Publishers
- L. Z. Yang, "Non-existence of meromorphic solution of a Fermat type functional equation", Aequationes Math, 76(1), pp.140~150 (2008)
- H. X. Yi, "A question of Gross and the uniqueness of entire functions", Nagoya Math. J, 138, pp.169~177 (1995)
- H. X. Yi, "Unicity theorems for meromorphic or entire functions", Bull. Austral. Math. Soc, 52(2), pp.215~224 (1995)
- H. X. Yi, "Unicity theorems for meromorphic or entire functions III", Bull. Austral. Math. Soc, 53(1), pp.71~82 (1996)
- H. X. Yi, "Meromorphic functions that share one or two values II", Kodai Math. J, 22(2), pp.264~272 (1999)
- H. X. Yi, "Meromorphic functions that share two sets", Kodai Math. J, 20(2), pp.127~134 (1997)
- X. B. Zhang, "Uniqueness of meromorphic functions sharing a small function and some normality criteria", 박사, pp.2011
- J. L. Zhang, "On the Nevanlinna characteristic of f(qz) and its applications", J. Math. Anal. Appl, 369(2), pp.537~544 (2010)