Indeed, it was proved by Alspach [1] in 1981 that there is a non-expansive mapping on a non-void weakly compact

convex set into itself that is fixed point free.

v] in (8) is the smallest

convex set containing all data points; and [T.

3--X (A, b) is non-convex, but it is composed of several n-dimensional rectangular regions with each rectangular region being a closed

convex set [2].

n] [right arrow] R is convex if dom f is a

convex set and if for any x, y [member of] dom f and any [theta] [member of] R with 0 [less than or equal to] 9 [less than or equal to] 1, then

Thus, every

convex set is also an invex set with respect to (Eq.

In the second paper the authors Cai Huaxian, Tian Tian and Cai Yilin studied the optimization problem with nonlinear constrained

convex set by the application of nonlinear neural network.

n] be symmetric with non empty interior Harmonically

convex set and let [phi] : [OMEGA] [right arrow] [R.

Given a real Hausdorff topological vector space E, a closed

convex set X [[subset].

If the function H is univalent in U and H(U) is a

convex set, then

Unfortunately, the union of polytopes is not a

convex set.

Assuming that we have at our disposal an algorithm called CircumRatio(X,Y), determining the scale ratio to apply to a

convex set X to circumscribe it to a

convex set Y, the algorithm estimating the similarity degree between two shapes is the following:

Constraints on the strategies are described by a nonempty, closed,

convex set K, model which covers most cases of practical interest.