Abstract. We prove asymptotic formulas for best approximations of planar spindle convex sets by inscribed and circumscribed convex disc-polygons with respect to the Hausdorff metric, the area deviation, and the perimeter deviation.

AMS Subject Classification (1991): 52A10

Keyword(s): approximations, disc-polygons, spindle convexity

Received March 7, 2011, and in final form August 4, 2011. (Registered under 14/2011.)