iii) ([phi] * zf')/([phi] * z[psi]') takes all its values in a convex domain
D if f'/[psi]' takes all its values in D.
where F is a Frechet-differential operator defined on an open convex domain
D of a Banach space X with values in a Banach space Y.
First we give error estimates in case of a convex domain
By a convex domain
we mean an open set which contains the line segment joining any two points of it.
Namely, for any n-dimensional convex domain
there is the sharp inequality
where F: D [subset or equal to] X 6 X is an operator defined on an open convex domain
D of a Banach space X with values in X.
1], on a simple convex domain
which contain M, then
By reference , the convex domain
formed by the convex combination of all the point vectors of each expert can be seen as the feasible domain of the weight vector of order alternatives.
D] [Lambda] of the Dirichlet Laplacian in a bounded convex domain
[Omega] [element of] [R.
d] is a bounded, strictly convex domain
with boundary of class [C.
It is well-known that if an analytic function maps the unit disk D univalently onto a convex domain
, then it also maps each concentric subdisk onto a convex domain
He discusses in detail the Dirichlet problems for quasilinear and fully nonlinear elliptic equations of the second order: quasilinear uniformly elliptic equations in arbitrary domains, mean curvature equations in domains with non-negative boundary mean curvature, fully nonlinear uniformly elliptic equations in arbitrary domains, and Monge-Ampere equation in uniformly convex domains