Key Points:

Canterbury businessman Peter Maxwell Stewart's bid to overturn his convictions on historical sex abuse charges has been rejected by the Court of Appeal.

A High Court jury in Christchurch last December found him guilty of five charges of indecency with a child under 12 years, one count of sodomy, and one count of rape.

The sex offending dated back up to 40 years and led to a 3 1/2-year jail sentence.

Stewart appealed on the grounds that the trial was unfair.