Article Sidebar
Date Published:
27/02/2023
Online Published:
11/11/2022
Abstract Views: 105
Views PDF: 44
Views PDF: 44
Issue
Section
Articles
How to Cite
Vu, H. A. (2022). A NEW CLASS OF UNIQUE RANGE SETS FOR MEROMORPHIC FUNCTIONS IGNORING MULTIPLICITY WITH 15 ELEMENTS. Thang Long Journal of Science: Mathematics and Mathematical Sciences, 1(4), 103-115. https://science.thanglong.edu.vn/index.php/volc/article/view/52
A NEW CLASS OF UNIQUE RANGE SETS FOR MEROMORPHIC FUNCTIONS IGNORING MULTIPLICITY WITH 15 ELEMENTS
Main Article Content
Abstract
In this paper, we give a new class of unique range sets for meromorphic functions ignoring multiplicity with 15 elements.
Article Details
Keywords
Meromorphic Function, uniqueness, ignoring multiplicity.
References
[1] A. Banerjee, A new class of strong uniqueness polynomials satisfying Fujimotos conditions, Ann. Acad. Sci. Fenn. Math. Vol. 40, 2015, 465-474.
[2] S. Bartels, Meromorphic functions sharing a set with 17 elements ignoring multiplicities, Compl. Var. Theory Appl., 39, 8592 (1999).
[3] 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.
[5] G. Frank, and M. Reinders, A unique range set for meromorphic functions with 11 elements, Compl. Var. Theory Appl. 37:1, 1998, 185-193.
[6] H. Fujimoto, On uniqueness of meromorphic functions sharing finite sets, Amer. J. Math. 122, 2000, 1175-1203.
[7] H. Fujimoto, H. On uniqueness polynomials for meromorphic functions, Nagoya Math. J., 170, 3346 (2003).
[8] 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.
[9] 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.
[10] 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.
[11] 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.
[12] Ha Huy Khoai, Vu Hoai An and Le Quang Ninh, Value-sharing and unique- ness for L-functions , Ann. Polonici Math.,2021.
[13] 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).
[15] 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.
[16] H. X. Yi, Uniqueness of Meromorphic Functions and question of Gross, Sci. China (Ser. A), Vol.37 N0.7, July 1994, 802-813.
[17] H. X. Yi, A question of Gross and the uniqueness of entire functions, Nagoya Math. J. Vol. 138 (1995), 169-177.
[18] H. X. Yi, Unicity theorems for meromorphic and entire functions III, Bull. Austral. Math. Soc., 53, 7182 (1996).
[19] H. X. Yi, The reduced unique range sets for entire or meromorphic functions, Compl. Var. Theory Appl., 32, 191198 (1997).
[20] H. X. Yi, On a question of Gross concerning uniqueness of entire functions, Bull. Austral. Math. Soc. Vol. 57(1998), 343-349.
[21] H. X. Yi and W.C.Lin, Uniqueness theorems concerning a question of Gross, Proc. Japan Acad., Ser. A, 80, 2004, 136-140.
[2] S. Bartels, Meromorphic functions sharing a set with 17 elements ignoring multiplicities, Compl. Var. Theory Appl., 39, 8592 (1999).
[3] 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.
[5] G. Frank, and M. Reinders, A unique range set for meromorphic functions with 11 elements, Compl. Var. Theory Appl. 37:1, 1998, 185-193.
[6] H. Fujimoto, On uniqueness of meromorphic functions sharing finite sets, Amer. J. Math. 122, 2000, 1175-1203.
[7] H. Fujimoto, H. On uniqueness polynomials for meromorphic functions, Nagoya Math. J., 170, 3346 (2003).
[8] 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.
[9] 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.
[10] 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.
[11] 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.
[12] Ha Huy Khoai, Vu Hoai An and Le Quang Ninh, Value-sharing and unique- ness for L-functions , Ann. Polonici Math.,2021.
[13] 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).
[15] 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.
[16] H. X. Yi, Uniqueness of Meromorphic Functions and question of Gross, Sci. China (Ser. A), Vol.37 N0.7, July 1994, 802-813.
[17] H. X. Yi, A question of Gross and the uniqueness of entire functions, Nagoya Math. J. Vol. 138 (1995), 169-177.
[18] H. X. Yi, Unicity theorems for meromorphic and entire functions III, Bull. Austral. Math. Soc., 53, 7182 (1996).
[19] H. X. Yi, The reduced unique range sets for entire or meromorphic functions, Compl. Var. Theory Appl., 32, 191198 (1997).
[20] H. X. Yi, On a question of Gross concerning uniqueness of entire functions, Bull. Austral. Math. Soc. Vol. 57(1998), 343-349.
[21] H. X. Yi and W.C.Lin, Uniqueness theorems concerning a question of Gross, Proc. Japan Acad., Ser. A, 80, 2004, 136-140.