학술논문
Unbounded solutions of an iterative-difference equation
Document Type
article
Author
Source
Acta Universitatis Sapientiae: Mathematica, Vol 9, Iss 1, Pp 224-234 (2017)
Subject
Language
English
ISSN
2066-7752
Abstract
Unbounded solutions for the iterative-difference equation f2(x)=λf(x+a)+μx, 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.