Abstract
We make sharp estimates to obtain a Schwarz-type lemma for the symmetrized polydisc and for the extended symmetrized polydisc . We explicitly construct an interpolating function under certain condition. To do so, we followed the methods described in [Young NJ. The automorphism group of the tetrablock. J Lond Math Soc. 2008;77(2):757–770]. Also we find a few geometric interplay between the members of the family and its closure .
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