Abstract
Abstract This paper shows via a reduced family of examples, the relaxed Newton's method is applied to complex exponential function F ( z )= z e z and F ( z )= z e z 2 , the basin of roots has infinite area. In addition, we examined their computer pictures which are fractals for the relaxed Newton's basin. In fact, computer experiments F ( z )= P ( z )e z and F ( z )= P ( z )e z 2 , indicate this to hold for arbitrary non-constant polynomial P ( z ).
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