Browse > Article
http://dx.doi.org/10.14317/jami.2019.133

UNIQUENESS OF MEROMORPHIC FUNCTIONS CONCERNING THE SHIFTS AND DERIVATIVES  

MENG, CHAO (College of Science, Shenyang Aerospace University)
LIU, GANG (College of Science, Shenyang Aerospace University)
Publication Information
Journal of applied mathematics & informatics / v.37, no.1_2, 2019 , pp. 133-148 More about this Journal
Abstract
This paper is devoted to studying the sharing value problem for the derivative of a meromorphic function with its shift and q-difference. The results in the paper improve and generalize the recent result due to Qi, Li and Yang.
Keywords
meromorphic function; shift; uniqueness; weighted sharing;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
연도 인용수 순위
1 A. Al-Khaladi, On meromorphic functions that share one value with their derivative, Analysis 25(2005), 131-140.   DOI
2 A. Banerjee, Uniqueness of meromorphic functions that share two sets, Southeast Asian Bull. Math. 31(2007), 7-17.
3 K. Liu and X.J. Dong, Some results related to complex differential-di erence equations of certain types, Bull. Korean Math. Soc. 51(2014), 1453-1467.   DOI
4 L.P. Liu and Y.X. Gu, Uniqueness of meromorphic functions that share one small function with their derivatives, Kodai Math. J. 27(2004), 272-279.   DOI
5 F. Lu, J.F. Xu and H.X. Yi, Entire functions that share one value with their linear differential polynomials, J. Math. Anal. Appl. 342(2008) 615-628.   DOI
6 F. Lu and H.X. Yi, The Bruck conjecture and entire functions sharing polynomials with their k-th derivatives, J. Korean Math. Soc. 48(2011), 499-512.   DOI
7 C. Meng, On unicity of meromorphic function and its kth order derivative, J. Math. Inequal. 4(2010), 151-159.   DOI
8 D.C. Pramanik, M. Biswas and R. Mandal, On the study of Bruck conjecture and some non-linear complex differential equations, Arab J. Math. Sci. 23(2017), 196-204.   DOI
9 X.G. Qi, N. Li and L.Z. Yang, Uniqueness of meromorphic functions concerning their di erences and solutions of di erence painleve equations, Comput. Methods Funct. Theory. 18(2018), 567-582.   DOI
10 X.G. Qi and K. Liu, Uniqueness and value distribution of di erences of entire functions, J. Math. Anal. Appl. 379(2011), 180-187.   DOI
11 L.A. Rubel and C.C. Yang, Values shared by an entire function and its derivatives, In: Complex Analysis, Kentucky 1976 (Proc. Conf), Lecture Notes in Mathematics 599, Springer-Verlag, Berlin, 1977, 101-103.
12 Z.X. Chen, On the difference counterpart of Bruck conjecture, Acta Math. Sci. 34(2014), 653-659.   DOI
13 D.C. Barnett, R.G. Halburd, R.J. Korhonen and W. Morgan, Nevanlinna theory for the q-difference operator and meromorphic solutions of q-difference equations, Proc. Roy. Soc. Edinburgh Sect. A 137(2007), 457-474.   DOI
14 R. Bruck, On entire functions which share one value CM with their first derivative, Results Math. 30(1996), 21-24.   DOI
15 J.M. Chang and Y.Z. Zhu, Entire functions that share a small function with their derivatives, J. Math. Anal. Appl. 351(2009), 491-496.   DOI
16 Z.X. Chen and K.H. Shon, On conjecture of R. Bruck concerning the entire function sharing one value CM with its derivatives, Taiwanese J. Math. 8(2004), 235-244.   DOI
17 Z.X. Chen and H.X. Yi, On sharing values of meromorphic functions and their differences, Results Math. 63(2013), 557-565. .   DOI
18 Y.M. Chiang and S.J. Feng, On the Nevanlinna characteristic of f(z + $\eta$) and difference equations in the complex plane, Ramanujan J. 16(2008), 105-129.   DOI
19 X.J. Dong and K. Liu,Some results on differential-difference analogues of Bruck conjecture, Math. Slovaca 67(2017), 691-700.   DOI
20 J. Grahl and C. Meng, Entire functions sharing a polynomial with their derivatives and normal families, Analysis 28(2008), 51-61.   DOI
21 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), 88-95.   DOI
22 R.G. Halburd and R.J. Korhonen, Nevanlinna theory for the difference operator, Ann. Acad. Sci. Fenn. Math. 31(2006), 463-478.
23 L.Z. Yang, Further results on entire functions that share one value with their derivatives, J. Math. Anal. Appl. 212(1997) 529-536.   DOI
24 J.P. Wang, Entire functions that share a polynomial with one of their derivatives, Kodai Math. J. 27(2004), 144-151.   DOI
25 J.P. Wang and H.X. Yi, Entire functions that share one value CM with their derivatives, J. Math. Anal. Appl. 277(2003) 155-163.   DOI
26 L.Z. Yang, Solution of a di erential equation and its applications, Kodai Math. J. 22(1999), 458-464.   DOI
27 L. Yang, Value distribution theory, Springer-Verlag, Berlin, 1993.
28 K.W. Yu, On entire and meromorphic functions that share small functions with their derivatives, J. Inequal. Pure Appl. Math. 4(1)(2003), Art. 21.
29 J. Zhang and L.W. Liao, Entire functions sharing some values with their di erence operators, Sci. China Math. 57(2014), 2143-2152.   DOI
30 J.L. Zhang, Meromorphic functions sharing a small function with their derivatives, Kyungpook Math. J. 49(2009), 143-154.   DOI
31 J.L. Zhang and R.J. Korhonen, On the Nevanlinna characteristic of f(qz) and its applications, J. Math. Anal. Appl. 369(2010), 537-544.   DOI
32 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.
33 J.L. Zhang and L.Z. Yang, A power of an entire function sharing one value with its derivative, Comput. Math. Appl. 60(2010), 2153-2160.   DOI
34 C.C. Yang, On de ciencies of di erential polynomials, Math. Z. 125(1972), 107-112.   DOI
35 I. Lahiri, Uniqueness of a meromorphic function and its derivative, J. Inequal. Pure Appl. Math. 5(1)(2004), Art. 20.
36 W.K. Hayman, Meromorphic Functions, Clarendon, Oxford, 1964.
37 J. Heittokangas, R.J. Korhonen, R. Laine, I. Rieppo and J.L. Zhang, Value sharing results for shifts of meromorphic functions and sucient conditions for periodicity, J. Math. Anal. Appl. 355(2009), 352-363.   DOI
38 I. Lahiri, Weighted sharing and uniqueness of meromorphic functions, Nagoya Math. J. 161(2001), 193-206.   DOI
39 P. Li, Entire functions that share one value with their linear differential polynomials, Kodai Math. J. 22(1999) 446-457.   DOI
40 S. Li and Z.S. Gao, Entire functions sharing one or two finite values CM with their shifts or difference operators, Arch. Math. 97(2011), 475-483.   DOI
41 X.M. Li, C.Y. Kang, H.X. Yi, Uniqueness theorems for entire functions sharing a nonzero complex number with their difference operators, Arch. Math. 96(2011), 577-587.   DOI
42 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. 99(2012), 261-270.   DOI
43 Q.C. Zhang, Meromorphic function that share one small function with its derivative, J. Inequal. Pure Appl. Math. 6(4)(2005), Art. 116.
44 J.L. Zhang and L.Z. Yang, Some results related to a conjecture of R. Bruck, J. Inequal. Pure Appl. Math. 8(1)(2007), Art. 18.