Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
11010190 | Journal of Mathematical Analysis and Applications | 2019 | 14 Pages |
Abstract
In this paper, the two-parameter family Fbâ¡{fλ,μ(z)=λbz+μbâzforzâC:λâ¥Î¼>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,μâFb 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(lnâ¡b)2â¤lnâ¡(1+1+4λμ(lnâ¡b)22λlnâ¡b) and the Julia set is the whole of extended complex plane for 1+4λμ(lnâ¡b)2>lnâ¡(1+1+4λμ(lnâ¡b)22λlnâ¡b).
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Madhusudan Bera, M. Guru Prem Prasad,