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Banerjee, Abhijit
- A Uniqueness Result Related to Meromorphic Functions Sharing Two Sets II
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Authors
Affiliations
1 Department of Mathematics, University of Kalyani, West Bengal 741 235, IN
2 Department of Mathematics, Katwa College, Burdwan, 713 130, IN
1 Department of Mathematics, University of Kalyani, West Bengal 741 235, IN
2 Department of Mathematics, Katwa College, Burdwan, 713 130, IN
Source
The Journal of the Indian Mathematical Society, Vol 81, No 1-2 (2014), Pagination: 1-12Abstract
We use the notion of weighted sharing of sets to prove a uniqueness theorem for meromorphic functions sharing two sets which improve and supplement a recent result of the present authors.Keywords
Meromorphic Functions, Weighted Sharing, Shared Set.
- On the Uniqueness of Power of a Meromorphic Function Sharing a Set with its k-th Derivative
Abstract Views :358 |
PDF Views:9
Authors
Affiliations
1 Department of Mathematics, University of Kalyani, 741235, IN
1 Department of Mathematics, University of Kalyani, 741235, IN
Source
The Journal of the Indian Mathematical Society, Vol 85, No 1-2 (2018), Pagination: 1-15Abstract
In the existing literature, many researchers consider the uniqueness of the power of a meromorphic function with its derivative counterpart share certain values or small functions. Here we consider the same problem under the aegis of a more general settings namely set sharing.
Keywords
Meromorphic Function, Set Sharing, Uniqueness.References
- A. Banerjee, Uniqueness of meromorphic functions sharing two sets with nite weight II, Tamkang J. Math., 41(4) (2010), 379-392.
- A. Banerjee and B. Chakraborty, A new type of unique range set with decient values, Afr. Mat., 26(7-8) (2015), 1561-1572.
- A. Banerjee and B. Chakraborty, Uniqueness of the power of a meromorphic functions with its dierential polynomial sharing a set, Math. Morav., 20(2) (2016), 1-14.
- A. Banerjee and B. Chakraborty, Further results on the uniqueness of meromorphic functions and their derivative counterpart sharing one or two sets, Jordan J. Math. Stat., 9(2) (2016), 117-139.
- W. K. Hayman, Meromorphic Functions, The Clarendon Press, Oxford (1964).
- I. Lahiri, Weighted sharing and uniqueness of meromorphic functions, Nagoya Math. J., 161 (2001), 193-206.
- A. Z. Mokhon'ko, On the Nevanlinna characteristics of some meromorphic functions, in Theory of Functions, functional analysis and their applications", Izd-vo Khar'kovsk, Un-ta, 14 (1971), 83-87.
- E. Mues and N. Steinmetz, Meromorphe Funktionen die unit ihrer Ableitung Werte teilen, Manuscripta Math., 29 (1979) 195-206.
- L. A. Rubel and C. C. Yang, Values shared by an entire function and its derivative, Complex analysis (Proc. Conf., Univ. Kentucky, Lexington, Ky., 1976), Lecture Notes in Math., 599 (1977), 101-103, Springer, Berlin.
- L. Z. Yang and J. L. Zhang, Non-existance of meromorphic solutions of Fermat type functional equation, Aequations Math., 76 (2008), 140-150.
- H. X. Yi and W. C. Lin, Uniqueness theorems concerning a question of Gross, Proc. Japan Acad., 80, Ser.A (2004), 136-140.
- J. L. Zhang, Meromorphic functions sharing a small function with their derivatives, Kyungpook Math. J., 49 (2009), 143-154.
- J. L. Zhang and L. Z. Yang, A power of a meromorphic function sharing a small function with its derivative, Ann. Acad. Sci. Fenn. Math., 34 (2009), 249-260.
- H. X. Yi, On a question of Gross concerning uniqueness of entire functions, Bull. Austral. Math. Soc., 57 (1998), 343-349.
- Generalization on the Question of C. C. Yang in the Light of Weighted Shared Sets
Abstract Views :383 |
PDF Views:4
Authors
Affiliations
1 Department of Mathematics, University of Kalyani, IN
2 Department of Mathematics, Kalipada Ghosh Tarai Mahavidyalaya, IN
1 Department of Mathematics, University of Kalyani, IN
2 Department of Mathematics, Kalipada Ghosh Tarai Mahavidyalaya, IN
Source
The Journal of the Indian Mathematical Society, Vol 86, No 1-2 (2019), Pagination: 1-21Abstract
In this paper, with the help of weighted sharing method, we have extended the question of Yang [8] from value sharing to set sharing which in turn have improved the results of Li-Gu [6] and Yi [10, 11] to a large extent.Keywords
Meromorphic Function, Derivative, Small Function, Weighted Sharing, Shared Sets.References
- A. Banerjee, Meromorphic functions sharing one value, Int. J. Math. Math. Sci., 22(2005), 3587 - 3598.
- W. K. Hayman, Meromorphic functions, Oxford, Clarendon Press, 1964.
- I. Lahiri, Weighted sharing and uniqueness of meromorphic functions, Nagoya Math. J., 16(1)(2001), 193-206.
- I. Lahiri, Weighted value sharing and uniqueness of meromorphic functions, Complex Var. Theory Appl., 46(2001), 241-253.
- I. Lahiri and A. Sarkar, Uniqueness of meromorphic function and its derivative, J. Inequal. Pure Appl. Math., 5 (1)(2004), Art.20 [ONLINE http://jipam.vu.edu.au/].
- J. T. Li and Y. X Gu, On uniqueness of meromorphic functions and their derivatives, Acta Mathematica Sinica (Chinese Series), 43(1)(2000), 87-94.
- P. Li and C. C. Yang, Some further results on the unique range sets of meromorphic functions, Kodai Math. J., 18(1995), 437-450.
- C. C. Yang, On two entire functions which together with their first derivatives have the same zero, J. Math. Anal. Appl., 56(1976), 1-6.
- L. Yang, Value Distribution Theory, Springer-verlag, Berlin.
- H. X. Yi, A question of C. C. Yang on the uniqueness of entire functions, Kodai Math. J., 13(1)(1990), 39-46.
- H. X. Yi, Uniqueness of meromorphic function and a question of C. C. Yang, Complex Var. Theory Appl., 14(2)(1990), 169-176.
- H. X. Yi, Unicity theorems for meromorphic function whose n-th derivatives share the same 1-points, Complex Var. Theory Appl., 34(1997), 421-436.
- H. X. Yi, On characteristic function of a meromorphic function and its derivative, Indian J. Math., 33(2)(1991), 119-133.
- H. X. Yi and C. C. Yang, Uniqueness theory of meromorphic functions. Science Press/Kluwer Academic Publishers, Beijing/ New York.(1995/2003).
- Q. C. Zhang, Meromorphic function that shares one small function with its derivative, J. Inequal. Pure Appl. Math., 6(4)(2005), Art.116 [ ONLINE http://jipam.vu.edu.au/].
- Uniqueness of Meromorphic Functions Ordinarily and Partially Sharing Values With Reduced Linear C-shift Operators
Abstract Views :398 |
PDF Views:0
Authors
Affiliations
1 Department of Mathematics, University of Kalyani, Kalyani 741235, IN
1 Department of Mathematics, University of Kalyani, Kalyani 741235, IN
Source
The Journal of the Indian Mathematical Society, Vol 88, No 3-4 (2021), Pagination: 201–216Abstract
In this paper, we investigate the uniqueness problem of meromorphic functions ordinarily and partially sharing values with the reduced linear c-shift operators governed by them, which practically provide an extensions and improvements of a number of recent results at a large extent.Keywords
Meromorphic functions, uniqueness, reduced linear c-shift operator, partially shared valueReferences
- A. Banerjee and S. Bhattacharyya, Uniqueness of meromorphic functions with their reduced linear c-shift operators sharing two or more values or sets, Adv. Differ. Equ., 509 (2019), 1-23.
- S. Chen, On uniqueness of meromorphic functions and their di erence operators with partially shared values, Comput. Methods Funct. Theory, 18 (3)(2018), 529-536.
- Y. M. Chiang and S. J. Feng, On the Nevanlinna Characteristic f(z +) and difference equations in complex plane, Ramanujan J., 16 (2008), 105-129.
- R. G. Halburd and R. J. Korhonen, Nevanlinna theory for the di erence operator, Ann. Acad. Sci. Fenn. Math., 31 (2)(2006), 463-478.
- R. G. Halburd and R. J. Korhonen, Di erence analogue of the lemma on the logarithmic derivative with applications to di erence equations, J. Math. Anal. Appl., 314 (2006), 477-487.
- W. K. Hayman, Meromorphic Functions, The Clarendon Press, Oxford 1964.
- I. Lahiri, Weighted sharing and uniqueness of meromorphic functions, Nagoya Math. J., 161. (2001), 193-206.
- I. Lahiri, Weighted value sharing and uniqueness of meromorphic functions, Complex Var. Theo. Appl., 46 (2001), 241-253.
- S. Li, D. Mei and B. Chen, Uniqueness of meromorphic functions sharing two values with their difference operators, Adv. Di er. Equ., 390 (2017), 1-9.
- W. Lin, X. Lin and A. Wu, Meromorphic functions partially shared values with their shifts, Bull. Korean Math. Soc., 55 (2)(2018), 469-478.
- C. C. Yang and H. X. Yi, Uniqueness Theory of Meromorphic Functions, Kluwer Aca- demic Publishers, Dordrecht (2003).
- L. Yang, Value Distribution Theory, Springer, New York 1993.
- J. Zhang and L. W. Liao, Entire functions sharing some values with their di erence operators, Sci. China Math., 57 (10)(2014), 2143-2152.