Uniqueness of meromorphic functions ans Q-differential polynomials sharing small functions

Document Type: Research Paper

Author

Department of Mathematics‎, ‎Thai Nguyen University of Education‎, ‎Luong Ngoc Quyen Street‎, ‎Thai Nguyen City‎, ‎Viet Nam.

Abstract

‎The paper concerns interesting problems related to the field of Complex Analysis‎, ‎in particular, Nevanlinna theory of meromorphic‎ ‎functions‎. ‎We have studied certain uniqueness problem on differential polynomials of meromorphic functions sharing a‎ ‎small function‎. ‎Outside‎, ‎in this paper‎, ‎we also consider the uniqueness of $q-$ shift difference‎ - ‎differential polynomials‎ ‎of meromorphic functions sharing small function or a set in the complex plane.

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T.B. Cao, K. Liu and N. Xu, Zeros and uniqueness of Q-difference polynomials of meromorphic functions with zero order, Proc. Indian Acad. Sci. Math. Sci. 124 (2014), no. 4, 533--549.

M. Fang and Y. Wang, A Note on the Conjectures of Hayman, Mues and Gol'dberg, Comput. Methods Funct. Theory 13 (2013), no. 4, 533--543.

Z. Huang, Value distribution and uniqueness on q-differences of meromorphic functions, Bull. Korean Math. Soc. 50 (2013), no. 4, 1157--1171.

W. Lin and H. Yi, Uniqueness theorems for meromorphic functions, Indian. J. Pure Appl. Math. 35 (2004), no. 2, 121--132.

Q. Ling, L.R. Jie and X. Zuxing, Uniqueness of meromorphic functions sharing one small function, J. Comput. Appl. Math. 263 (2014) 225--235.

K. Liu and X. Qi, Meromorphic solutions of q-shift difference equations, Ann. Polon. Math. 101 (2011), no. 3, 215--225.

Y. Liu, J.P. Wang and F.H. Liu, Some results on value distribution of the difference operator, Bull. Iranian Math. Soc. 41 (2015), no. 3, 603--611.

X. Qi and L. Yang, Sharing sets of q-difference of meromorphic functions, Math. Slovaca 64 (2014), no. 1, 51--60.

N.V. Thin and H.T. Phuong, Uniqueness of meromorphic functions sharing a value or small function, Math. Slovaca 66 (2016), no. 4, 829--844.

N. Wu and Z. Xuan, On the uniqueness theory of algebroid functions in some proper domain, Bull. Iranian Math. Soc. 41 (2015), no. 6, 1315--1326.

J. Xu and X. Zhang, The zeros of q-shift difference polynomials of meromorphic functions, Adv. Difference Equ. 2012 (2012), no. 200, 10 pages.

X. Zhang, Value sharing of meromorphic functions and some questions of Dyavanal, Front. Math. China 7 (2012), no. 1, 161--176.

J. Zhang, H.Y. Kang and L.W. Liao, Entire functions sharing a small entire function with their difference operators, Bull. Iranian Math. Soc. 41 (2015), no. 5, 1121--1129.

J. Zhang and R. Korhonen, On the Nevanlinna characteristic of f(qz) and its applications, J. Math. Anal. Appl. 369 (2010), no. 2, 537--544.

Q. Zhao and J. Zhang, Zeros and shared one value of q-shift difference polynomials, J. Contemp. Math. Anal. 50 (2015), no. 2, 63--69.