In this note, first, we show that the asymptotic subcone, the ultralimit, the completion of an asymptotically PT-1 space are still an asymptotically PT-1 space. Secondly, we consider two kinds of metric spaces, which have been considered by Ibragimov and Gromov, respectively. We show that they are asymptotically PT-1 spaces under particular conditions, which provide some concrete examples of asymptotically PT
In this paper,we discuss the sense-preserving univalent harmonic mappings from the unit disk D onto asymmetrical vertical strips Ωα={ω：α-π/2sinαR（ω）α/2sinα},π/2≤απSuch results as analytic representation formula,coefficient estimates,distortion theorem and area theorem are derived.
