“…> 0. In [3], Mortini and Rhin raised the question of determining precisely the set D p = {c ∈ C : f p,c is a self-map of D} for p > 1. They proved that [0, 1] ⊆ D p for p ≥ 1.…”
We give a characterization of the sets Dp (1 < p < 2) of complex numbers c such that z → 1+z 2 + c 1−z 2 p is a self-map of the closed unit disk and we show that these sets are increasing with respect to p.
“…> 0. In [3], Mortini and Rhin raised the question of determining precisely the set D p = {c ∈ C : f p,c is a self-map of D} for p > 1. They proved that [0, 1] ⊆ D p for p ≥ 1.…”
We give a characterization of the sets Dp (1 < p < 2) of complex numbers c such that z → 1+z 2 + c 1−z 2 p is a self-map of the closed unit disk and we show that these sets are increasing with respect to p.
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