Abstract
Abstract
Let f be a transcendental meromorphic function of finite order and c be a nonzero complex number. Define $\Delta _{c}f=f(z+c)-f(z)$
Δ
c
f
=
f
(
z
+
c
)
−
f
(
z
)
. The authors investigate the existence on the fixed points of $\Delta _{c}f$
Δ
c
f
. The results obtained in this paper may be viewed as discrete analogues on the existing theorem on the fixed points of $f'$
f
′
. The existing theorem on the fixed points of $\Delta _{c}f$
Δ
c
f
generalizes the relevant results obtained by (Chen in Ann. Pol. Math. 109(2):153–163, 2013; Zhang and Chen in Acta Math. Sin. New Ser. 32(10):1189–1202, 2016; Cui and Yang in Acta Math. Sci. 33B(3):773–780, 2013) et al.
Funder
Natural Science Foundation of Hubei Provincial Department of Education
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Algebra and Number Theory,Analysis
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3. Chen, Z.X.: Fixed points of meromorphic functions and of their difference and shifts. Ann. Pol. Math. 109(2), 153–163 (2013)
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