Perhaps the earliest reference is this:
Chew & Drysdale. "Voronoi diagrams based on convex distance functions." 1985. (ACM link)
This more recent dissertation at the FernUniversität Hagen may be more directly useful:
Ma. "Bisectors and Voronoi Diagrams for Convex Distance Functions." 2000. (PDF download)
I extracted this figure from her thesis, p.58:
Google Scholar finds 42 papersfinds 42 papers post-2000 that cite this dissertation.