Open AccessMeromorphic solutions of higher order non-homogeneous linear difference equations
Author(s) -
Benharrat Belaïdi,
Rachid Bellaama
Publication year - 2020
Publication title -
bulletin of the "transilvania" university of braşov. series iii, mathematics, informatics, physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.203
H-Index - 5
eISSN - 2065-216X
pISSN - 2065-2151
DOI - 10.31926/but.mif.2020.13.62.2.6
Subject(s) - meromorphic function , order (exchange) , mathematics , homogeneous , zero (linguistics) , type (biology) , upper and lower bounds , mathematical analysis , combinatorics , ecology , linguistics , philosophy , finance , economics , biology
In this paper, we investigate the growth of meromorphic solutions of nonhomogeneous linear difference equation A_n(z)f(z + c_n) + · · · + A_1(z)f(z + c_1) + A_0(z)f(z) = A_{n+1}(z), where A_{n+1 (z), · · · , A0 (z) are (entire) or meromorphic functions and c_j (1, · · · , n) are non-zero distinct complex numbers. Under some conditions on the (lower) order and the (lower) type of the coefficients, we obtain estimates on the lower bound of the order of meromorphic solutions of the above equation. We extend early results due to Luo and Zheng.