Unbounded solutions of an iterative-difference equation

Lin Li; Pingping Zhang

doi:10.1515/ausm-2017-0015

Abstract

Unbounded solutions for the iterative-difference equation $f^{2} (x) = λ f (x + a) + μ x, x \in ℝ,$ \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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Unbounded solutions of an iterative-difference equation

Abstract

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