In this paper, our interest is devoted to study the convex combinations of form (1 ? ?) f + ?1, where (0, 1), biholomorphic mappings on Euclidean unit ball Bn in case several complex variables. Starting from a result proved by S. Trimble [26] and then extended P.N. Chichra R. Singh [3, Theorem 2] which says that if starlike such Re[f ?(z)] > 0, (1??)z+?f (z) also starlike, we are interested ...

We derive an upper bound on the generalization error of classi ers which can be represented as thresholded convex combinations of thresholded convex combinations of functions. Such classi ers include single hidden-layer threshold networks and voted combinations of decision trees (such as those produced by boosting algorithms). The derived bound depends on the proportion of training examples wit...

Let the invariant probability measures for an orientation-reversing weakly expanding map of the interval [0, 1] be partially ordered by majorization. The minimal elements of the resulting poset are shown to be convex combinations of Dirac measures supported on two adjacent fixed points. A consequence is that if f : [0, 1] → R is strictly convex, then either its minimizing measure is unique and ...