On the Biholomorphic Convex Mappings of Order Alpha on Dnp

In this paper, we first give the definition of biholomorphic convex mappings of order alpha on the Reinhardt domain D-p(n) in C-n. Next, we provide several sufficient conditions for it. Then we introduce a subclass SK( D-p(n), alpha) of biholomorphic convex mappings of order a on D-p(n), and give a necessary and sufficient condition for the subclass SK( D-p(n), alpha). From these, we construct some concrete examples of biholomorphic convex mappings of order alpha on D-p(n). The results presented extend the related results of earlier authors.