  Extending results of Hershberger and Suri for the Euclidean plane, we show
that ball hulls and ball intersections of sets of $n$ points in strictly convex
normed planes can be constructed in $O(n \log n)$ time. In addition, we confirm
that, like in the Euclidean subcase, the $2$-center problem with constrained
circles can be solved also for strictly convex normed planes in $O(n^2)$ time.
Some ideas for extending these results to more general types of normed planes
are also presented.
