Abstract
In this paper, the existing results concerning difference operator sharing two sets have been extended up to the most general form, namely linear difference operator. Furthermore, we have been able to find out the specific form of the function. A considerable number of examples have been exhibited throughout the paper pertinent with different issues.
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REFERENCES
A. Banerjee, ‘‘Meromorphic functions sharing two sets,’’ Czech. Math. J. 57 (132), 1199–1214 (2007).
A. Banerjee, ‘‘Uniqueness of meromorphic functions sharing two sets with finite weight II,’’ Tamkang J. Math. 41 (4), 379–392 (2010).
A. Banerjee and M. B. Ahamed, ‘‘On uniqueness of meromorphic functions sharing three sets with finite weights,’’ Bull. Polish Acad. Sci. Math. 62 (3), 243–256 (2014).
A. Banerjee and S. Bhattacharyya, ‘‘On the uniqueness of meromorphic functions and its difference operator sharing values or sets,’’ Rend. Circ. Mat. Palermo, II. https://doi.org/10.1007/s12215-016-0295-1.
B. Chen and Z. Chen, ‘‘Meromorphic functions sharing two sets with its difference operator,’’ Bull. Malays. Math. Soc. 35 (3), 765–774 (2012).
Y. M. Chiang and S. J. Feng, ‘‘On the Nevanlinna characteristic \(f(z+Q)\) and difference equation in complex plane,’’ Ramanujan J. 16, 105–129 (2008).
B. Deng, D. Liu and D. Yang, ‘‘Meromorphic functions and its difference operator share two sets with weight k,’’ Turkish J. Math. 41, 1155–1163 (2017).
R. G. Halburd and R. J. Korhonen, ‘‘Nevanlinna theory for the difference operator,’’ Ann. Acad. Sci. Fenn. Math. 31 (2), 463–478 (2006).
W. K. Hayman, Meromorphic Functions ( Clarendon Press, Oxford, 1964).
J. Heittokangas, R. Korhonen, I. Laine, J. Rieppo and J. L. Zhang, ‘‘Value sharing results for shifts of meromorphic function and sufficient conditions for periodicity,’’ J. Math. Anal. Appl. 355, 352–363 (2009).
I. Lahiri, ‘‘Weighted sharing and uniqueness of meromorphic functions,’’ Nagoya Math. J. 161, 193–206 (2001).
I. Lahiri, ‘‘Weighted value sharing and uniqueness of meromorphic functions,’’ Complex Var. Theory Appl. 46, 241–253 (2001).
I. Lahiri, ‘‘Value distribution of certain differential polynomials,’’ Int. J. Math. Math. Sci. 28 (2), 83–91 (2001).
I. Lahiri and A. Banerjee, ‘‘Weighted sharing of two sets,’’ Kyungpook Math. J. 46 (1), 79–87 (2006).
I. Lahiri and S. Dewan, ‘‘Value distribution of the product of a meromorphic function and its derivative,’’ Kodai Math. J. 26, 95–100 (2003).
I. Laine, Nevanlinna Theory and Complex Differential Equations (Walter de Gruyter, Berlin, 1993).
H. X. Yi, ‘‘Meromorphic functions that share three sets,’’ Kodai Math. J. 20, 22–32 (1997).
H. X. Yi, ‘‘Meromorphic functions that share one or two values II,’’ Kodai Math. J. 22, 264–272 (1999).
C. C. Yang, ‘‘On deficiencies of differential polynomials II,’’ Math. Z. 125, 107–112 (1972).
H. X. Yi and L. Z. Yang, ‘‘Meromorphic functions that share two sets,’’ Kodai Math. J. 20, 127–134 (1997).
J. Zhang, ‘‘Value distribution and shared sets of differences of meromorphic functions,’’ J. Math. Anal. Appl. 367 (2), 401–408 (2010).
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Banerjee, A., Basir Ahamed, M. Results on Meromorphic Function Sharing Two Sets with Its Linear \(\boldsymbol{c}\)-Difference Operator. J. Contemp. Mathemat. Anal. 55, 143–155 (2020). https://doi.org/10.3103/S1068362320030024
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DOI: https://doi.org/10.3103/S1068362320030024