Browse > Article
http://dx.doi.org/10.4134/BKMS.b200840

MEROMORPHIC FUNCTION PARTIALLY SHARES SMALL FUNCTIONS OR VALUES WITH ITS LINEAR c-SHIFT OPERATOR  

Banerjee, Abhijit (Department of Mathematics University of Kalyani)
Maity, Sayantan (Department of Mathematics University of Kalyani)
Publication Information
Bulletin of the Korean Mathematical Society / v.58, no.5, 2021 , pp. 1175-1192 More about this Journal
Abstract
In this paper, we have studied on the uniqueness problems of meromorphic functions with its linear c-shift operator in the light of partial sharing. Our two results improve and generalize two very recent results of Noulorvang-Pham [Bull. Korean Math. Soc. 57 (2020), no. 5, 1083-1094] in some sense. In addition, our other results have improved and generalized a series of results due to Lü-Lü [Comput. Methods Funct. Theo. 17 (2017), no. 3, 395-403], Zhen [J. Contemp. Math. Anal. 54 (2019), no. 5, 296-301] and Banerjee-Bhattacharyya [Adv. Differ. Equ. 509 (2019), 1-23]. We have exhibited a number of examples to show that some conditions used in our results are essential.
Keywords
Meromorphic function; uniqueness; linear c-shift operator; partial sharing; small function;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 Z.-X. Chen and H.-X. Yi, On sharing values of meromorphic functions and their differences, Results Math. 63 (2013), no. 1-2, 557-565. https://doi.org/10.1007/s00025-011-0217-7   DOI
2 R. G. Halburd and R. J. Korhonen, Difference analogue of the lemma on the logarithmic derivative with applications to difference equations, J. Math. Anal. Appl. 314 (2006), no. 2, 477-487. https://doi.org/10.1016/j.jmaa.2005.04.010   DOI
3 R. G. Halburd and R. J. Korhonen, Nevanlinna theory for the difference operator, Ann. Acad. Sci. Fenn. Math. 31 (2006), no. 2, 463-478.
4 R. G. Halburd and R. J. Korhonen, Value distribution and linear operators, Proc. Edinb. Math. Soc. 57 (2014), 493-504.   DOI
5 W. K. Hayman, Meromorphic Functions, Oxford Mathematical Monographs, Clarendon Press, Oxford, 1964.
6 J. Heittokangas, R. Korhonen, I. Laine, J. Rieppo, and J. Zhang, Value sharing results for shifts of meromorphic functions, and sufficient conditions for periodicity, J. Math. Anal. Appl. 355 (2009), no. 1, 352-363. https://doi.org/10.1016/j.jmaa.2009.01.053   DOI
7 Z.-B. Huang, Value distribution and uniqueness on q-differences of meromorphic functions, Bull. Korean Math. Soc. 50 (2013), no. 4, 1157-1171. https://doi.org/10.4134/BKMS.2013.50.4.1157   DOI
8 J. Zhang and L. Liao, Entire functions sharing some values with their difference operators, Sci. China Math. 57 (2014), no. 10, 2143-2152. https://doi.org/10.1007/s11425-014-4848-5   DOI
9 X.-M. Li, H.-X. Yi, and C.-Y. Kang, Notes on entire functions sharing an entire function of a smaller order with their difference operators, Arch. Math. (Basel) 99 (2012), no. 3, 261-270. https://doi.org/10.1007/s00013-012-0425-8   DOI
10 V. Noulorvang and D. T. Pham, On partial value sharing results of meromorphic functions with their shifts and its applications, Bull. Korean Math. Soc. 57 (2020), no. 5, 1083-1094. https://doi.org/10.4134/BKMS.b190483   DOI
11 Y.-M. Chiang and S.-J. Feng, On the Nevanlinna characteristic of f(z+η) and difference equations in the complex plane, Ramanujan J. 16 (2008), no. 1, 105-129. https://doi.org/10.1007/s11139-007-9101-1   DOI
12 R. Halburd, R. Korhonen, and K. Tohge, Holomorphic curves with shift-invariant hyperplane preimages, Trans. Amer. Math. Soc. 366 (2014), no. 8, 4267-4298. https://doi.org/10.1090/S0002-9947-2014-05949-7   DOI
13 X. Luo and W.-C. Lin, Value sharing results for shifts of meromorphic functions, J. Math. Anal. Appl. 377 (2011), no. 2, 441-449. https://doi.org/10.1016/j.jmaa.2010.10.055   DOI
14 Z.-B. Huang and R.-R. Zhang, Uniqueness of the differences of meromorphic functions, Anal. Math. 44 (2018), no. 4, 461-473. https://doi.org/10.1007/s10476-018-0306-x   DOI
15 Y. Jiang and Z. Chen, Meromorphic functions share two values with its difference operator, An. Stiint. Univ. Al. I. Cuza Iasi. Mat. (N.S.) 63 (2017), no. 1, 169-175.
16 F. Lu and W. Lu, Meromorphic functions sharing three values with their difference operators, Comput. Methods Funct. Theory 17 (2017), no. 3, 395-403. https://doi.org/10.1007/s40315-016-0188-5   DOI
17 K. Yamanoi, The second main theorem for small functions and related problems, Acta Math. 192 (2004), no. 2, 225-294. https://doi.org/10.1007/BF02392741   DOI
18 C.-C. Yang and H.-X. Yi, Uniqueness Theory of Meromorphic Functions, Mathematics and its Applications, 557, Kluwer Academic Publishers Group, Dordrecht, 2003.
19 L. Zhen, Meromorphic functions sharing three polynomials with their difference operators, J. Contemp. Math. Anal. 54 (2019), no. 5, 296-301; translated from Izv. Nats. Akad. Nauk Armenii Mat. 54 (2019), no. 5, 44-52.   DOI
20 J. Heittokangas, R. Korhonen, I. Laine, J. Rieppo, and J. Zhang, Uniqueness of meromorphic functions sharing values with their shifts, Complex Var. Elliptic Equ. 56 (2011), no. 1-4, 81-92. https://doi.org/10.1080/17476930903394770   DOI
21 C.-X. Chen and Z.-X. Chen, A note on entire functions and their differences, J. Inequal. Appl. 2013 (2013), 587, 17 pp. https://doi.org/10.1186/1029-242x-2013-587   DOI
22 A. Banerjee and S. Bhattacharyya, Uniqueness of meromorphic functions with their reduced linear c-shift operators sharing two or more values or sets, Adv. Difference Equ. 2019 (2019), Paper No. 509, 23 pp. https://doi.org/10.1186/s13662-019-2425-5   DOI
23 K. S. Charak, R. J. Korhonen, and G. Kumar, A note on partial sharing of values of meromorphic functions with their shifts, J. Math. Anal. Appl. 435 (2016), no. 2, 1241-1248. https://doi.org/10.1016/j.jmaa.2015.10.069   DOI