Affiliation:
1. College of Mathematics , Physics and Information Engineering Jiaxing University , P. R. China
2. Department of Mathematics , Binzhou University , P. R. China
Abstract
Abstract
Unbounded solutions for the iterative-difference equation
f
2
(
x
)
=
λ
f
(
x
+
a
)
+
μ
x
,
x
∈
ℝ
,
\font\msbm=MSBM10$${\rm{f}}^2 ({\rm{x}}) = \lambda {\rm{f}}({\rm{x}} + {\rm{a}}) + \mu {\rm{x}},\;\;\;{\rm{x}} \in {\msbm R},$$
have been considered in [Continuous solutions of an iterative-difference equation and Brillouët problem, Publ. Math. Debrecen, 78 (2011), 613–624], where λ, μ, a are real constants. In this paper, we continue to study the solutions not being included there, and further give the convex and concave ones. Finally, continuous solutions of this equation with an extra item were also given, which continuously depend on the parameter a.
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