Article ID Journal Published Year Pages File Type
11010190 Journal of Mathematical Analysis and Applications 2019 14 Pages PDF
Abstract
In this paper, the two-parameter family Fb≡{fλ,μ(z)=λbz+μb−zforz∈C:λ≥μ>0} of transcendental entire functions is considered. By investigating on the existence and nature of the fixed points of fλ,μ, the dynamics of functions fλ,μ∈Fb is studied. It is shown that the Julia set of fλ,μ is nowhere dense and not locally connected whenever parameters λ and μ satisfy 1+4λμ(ln⁡b)2≤ln⁡(1+1+4λμ(ln⁡b)22λln⁡b) and the Julia set is the whole of extended complex plane for 1+4λμ(ln⁡b)2>ln⁡(1+1+4λμ(ln⁡b)22λln⁡b).
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Physical Sciences and Engineering Mathematics Analysis
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