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Unbounded solutions of an iterative-difference equation

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Unbounded solutions for the iterative-difference equation f2(x)=λf(x+a)+μx,x,\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.

eISSN:
2066-7752
Langue:
Anglais
Périodicité:
2 fois par an
Sujets de la revue:
Mathematics, General Mathematics