A NEW CLASS OF UNIQUE RANGE SETS FOR MEROMORPHIC FUNCTIONS IGNORING MULTIPLICITY WITH 15 ELEMENTS

Tạp chí Khoa học Thăng Long - Tập 1 Số 4 - Trang 103-115 - 2022
Hoai An Vu1,2
1Hai Duong Pedagogical College
2Institute of Mathematics and Applied Sciences - Thang Long University

Tóm tắt

In this paper, we give a new class of unique range sets for meromorphic functions ignoring multiplicity with 15 elements.

Từ khóa

#Meromorphic Function #uniqueness #ignoring multiplicity.

Tài liệu tham khảo

A. Banerjee, A new class of strong uniqueness polynomials satisfying Fujimotos conditions, Ann. Acad. Sci. Fenn. Math. Vol. 40, 2015, 465-474.

S. Bartels, Meromorphic functions sharing a set with 17 elements ignoring multiplicities, Compl. Var. Theory Appl., 39, 8592 (1999).

B. Chakraborty, On the Cardinality of a Reduced Unique-Range Set, Ukr. Math. J., Vol. 72, No. 11, April, 2021, DOI 10.1007/s11253-021-01889-z. [4] A. A. Goldberg and I. V. Ostrovskii, Value Distribution of Meromorphic Functions, Translations of Mathematical Monographs (2008), V.236.

G. Frank, and M. Reinders, A unique range set for meromorphic functions with 11 elements, Compl. Var. Theory Appl. 37:1, 1998, 185-193.

H. Fujimoto, On uniqueness of meromorphic functions sharing finite sets, Amer. J. Math. 122, 2000, 1175-1203.

H. Fujimoto, H. On uniqueness polynomials for meromorphic functions, Nagoya Math. J., 170, 3346 (2003).

F. Gross, Factorization of meromorphic functions and some open problems, Complex Analysis (Proc. Conf . Univ. Kentucky, Lexington, Ky. 1976), pp. 51-69, Lecture Notes in Math. Vol. 599, Springer, Berlin, 1977.

Ha Huy Khoai, Some remarks on the genericity of unique range sets for meromorphic functions, Sci. China Ser. A Mathematics, Vol. 48, 2005, 262-267.

Ha Huy Khoai, Vu Hoai An, and Pham Ngoc Hoa, On functional equations for meromorphic functions and applications, Arch. Math, DOI 10.1007/s00013- 017-1093-5, 2017.

Ha Huy Khoai, Vu Hoai An and Nguyen Xuan Lai, Strong uniqueness polynomials of degree 6 and unique range sets for powers of meromorphic functions, Intern. J. Math., 2018, DOI:10.1142/S0129167X18500374.

Ha Huy Khoai, Vu Hoai An and Le Quang Ninh, Value-sharing and unique- ness for L-functions , Ann. Polonici Math.,2021.

Ha Huy Khoai and Vu Hoai An, Determining an L-function in the ex- tended Selberg class by its preimages of subsets, Ramanujan Journal, doi.org/10.1007/s11139-021-00483-y,2021. [14] W. K. Hayman, Meromorphic Functions, Clarendon, Oxford (1964).

P. Li, P., and C.-C. Yang, Some further results on the unique range sets of meromorphic functions, Kodai Math. J. 18, 1995, 437-450.

H. X. Yi, Uniqueness of Meromorphic Functions and question of Gross, Sci. China (Ser. A), Vol.37 N0.7, July 1994, 802-813.

H. X. Yi, A question of Gross and the uniqueness of entire functions, Nagoya Math. J. Vol. 138 (1995), 169-177.

H. X. Yi, Unicity theorems for meromorphic and entire functions III, Bull. Austral. Math. Soc., 53, 7182 (1996).

H. X. Yi, The reduced unique range sets for entire or meromorphic functions, Compl. Var. Theory Appl., 32, 191198 (1997).

H. X. Yi, On a question of Gross concerning uniqueness of entire functions, Bull. Austral. Math. Soc. Vol. 57(1998), 343-349.

H. X. Yi and W.C.Lin, Uniqueness theorems concerning a question of Gross, Proc. Japan Acad., Ser. A, 80, 2004, 136-140.