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, i.

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 [4], 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 (cf.

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.