Entire function sharing a small function with its mixed-operators
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Xianjing Dong
Abstract
In this article, we investigate the uniqueness problem on a transcendental entire function
Funding source: National Natural Science Foundation of China
Award Identifier / Grant number: 11661052
Award Identifier / Grant number: 11301260
Funding source: Natural Science Foundation of Jiangxi Province
Award Identifier / Grant number: 20161BAB211005
Award Identifier / Grant number: 20132BAB211003
Funding statement: This work was partially supported by the NSFC (nos. 11661052, 11301260), the NSF of Jiangxi (nos. 20161BAB211005, 20132BAB211003).
Acknowledgements
The authors would like to thank the referee for his/her helpful suggestions and comments.
References
[1] W. Bergweiler and J. K. Langley, Zeros of differences of meromorphic functions, Math. Proc. Cambridge Philos. Soc. 142 (2007), no. 1, 133–147. 10.1017/S0305004106009777Search in Google Scholar
[2] R. Brück, On entire functions which share one value CM with their first derivative, Results Math. 30 (1996), no. 1–2, 21–24. 10.1007/BF03322176Search in Google Scholar
[3] C. X. Chen and Z. X. Chen, Entire functions and their higher order differences, Taiwanese J. Math. 18 (2014), no. 3, 711–729. 10.11650/tjm.18.2014.3453Search in Google Scholar
[4] Z. X. Chen, On the difference counterpart of Brück’s conjecture, Acta Math. Sci. Ser. B Engl. Ed. 34 (2014), no. 3, 653–659. 10.1016/S0252-9602(14)60037-0Search in Google Scholar
[5] Z. X. Chen and K. H. Shon, On conjecture of R. Brück concerning the entire function sharing one value CM with its derivative, Taiwanese J. Math. 8 (2004), no. 2, 235–244. 10.11650/twjm/1500407625Search in Google Scholar
[6]
Y. M. Chiang and S. J. Feng,
On the Nevanlinna characteristic of
[7] F. Gross, Factorization of Meromorphic Functions, Mathematics Research Center, Washington, 1972. 10.1090/S0002-9947-1972-0301175-2Search in Google Scholar
[8] G. G. Gundersen, Estimates for the logarithmic derivative of a meromorphic function, plus similar estimates, J. Lond. Math. Soc. (2) 37 (1988), no. 1, 88–104. 10.1112/jlms/s2-37.121.88Search in Google Scholar
[9] G. G. Gundersen and L. Z. Yang, Entire functions that share one value with one or two of their derivatives, J. Math. Anal. Appl. 223 (1998), no. 1, 88–95. 10.1006/jmaa.1998.5959Search in Google Scholar
[10] 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. 10.1016/j.jmaa.2005.04.010Search in Google Scholar
[11] W. K. Hayman, Meromorphic Functions, Oxford Math. Monogr., Clarendon Press, Oxford, 1964. Search in Google Scholar
[12] 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. 10.1016/j.jmaa.2009.01.053Search in Google Scholar
[13] I. Laine, Nevanlinna Theory and Complex Differential Equations, De Gruyter Stud. Math. 15, Walter de Gruyter & Co., Berlin, 1993. 10.1515/9783110863147Search in Google Scholar
[14] I. Laine and C. C. Yang, Clunie theorems for difference and q-difference polynomials, J. Lond. Math. Soc. (2) 76 (2007), no. 3, 556–566. 10.1112/jlms/jdm073Search in Google Scholar
[15] S. Li and Z. S. Gao, A note on the Brück conjecture, Arch. Math. (Basel) 95 (2010), no. 3, 257–268; erratum, Arch. Math. (Basel) 99 (2012), no. 3, 255–259. 10.1007/s00013-010-0165-6Search in Google Scholar
[16] X. M. Li, C. Y. Kang and H. X. Yi, Uniqueness theorems of entire functions sharing a non-zero complex number with their difference operators, Arch. Math. (Basel) 96 (2011), no. 6, 577–587. 10.1007/s00013-011-0228-3Search in Google Scholar
[17] 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. 10.1007/s00013-012-0425-8Search in Google Scholar
[18] K. Liu and X. J. Dong, Some results related to complex differential-difference equations of certain types, Bull. Korean Math. Soc. 51 (2014), no. 5, 1453–1467. 10.4134/BKMS.2014.51.5.1453Search in Google Scholar
[19] K. Liu and L. Z. Yang, Value distribution of the difference operator, Arch. Math. (Basel) 92 (2009), no. 3, 270–278. 10.1007/s00013-009-2895-xSearch in Google Scholar
[20] C. C. Yang and H. X. Yi, Uniqueness Theory of Meromorphic Functions, Math. Appl. 557, Kluwer Academic Publishers, Dordrecht, 2003. 10.1007/978-94-017-3626-8Search in Google Scholar
[21] J. Zhang and L. W. Liao, Entire functions sharing some values with their difference operators, Sci. China Math. 57 (2014), no. 10, 2143–2152. 10.1007/s11425-014-4848-5Search in Google Scholar
[22] J. Zhang, J. J. Zhang and L. W. Liao, Entire functions sharing zero CM with their high order difference operators, Taiwanese J. Math. 18 (2014), no. 3, 701–709. 10.11650/tjm.18.2014.3802Search in Google Scholar
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Articles in the same Issue
- Frontmatter
- Well-posedness and a general decay for a nonlinear damped porous thermoelastic system with second sound
- Isomorphism classes of weighted spaces of holomorphic functions on some subsets of complex plane
- Asymptotic behavior of solutions of fractional nabla q-difference equations
- A decomposition theorem for locally compact groups
- An a posteriori truncation regularization method for an ill-posed problem for the heat equation with an integral boundary condition
- Entire function sharing a small function with its mixed-operators
- Hybrid projection method for a system of unrelated generalized mixed variational-like inequality problems
- On the full transitivity of a cotorsion hull
- Comparison results for solutions of elliptic Neumann problems with lower-order terms via Steiner symmetrization
- On the formula of Cohen–Vogt relatively pointed topological semi-simplicial sets
- On the boundedness of Marcinkiewicz integrals on continual variable exponent Herz spaces
- On the generalized absolute convergence of Fourier series
- Embedding theorems for Besov–Morrey spaces of many groups of variables
-
Projective flatness of a new class of
- Spread relation of E-valued meromorphic functions and its application
- q-dual mixed volumes and Lp-intersection bodies
