Keywords: Implicit iterative algorithm Asymptotically quasi-nonexpansive mappings Common fixed point Convex metric space a b s t r a c t In this paper, we consider an implicit iteration process to approximate the common fixed points of two finite families of asymptotically quasi-nonexpansive mappings in convex metric spaces. As a consequence of our result, we obtain some related convergence the...

We show the existence of sets with n points (n > 4) for which every convex decomposition contains more than f§« — § polygons, which refutes the conjecture that for every set of n points there is a convex decomposition with at most n + C polygons. For sets having exactly three extreme points we show that more than n + s/2(n 3) 4 polygons may be necessary to form a convex decomposition.

Let F be an arbitrary topological vector space; we shall say that a subset S of F is quasi-convex if the set of continuous affine functionals on 5 separates the points of S. If X is a Banach space and T: X -* F is a continuous linear operator, then T is quasi-convex if T(U) is quasiconvex, where U is the unit ball of X. In the case when T is compact, T(U) is quasi-convex if and only if it is af...

Let F = fC 1 ; C 2 ; : : : ; C n g be a family of n disjoint convex bodies in the plane. We say that a set V of exterior light sources illuminates F, if for every boundary point u of any member of F there is a point v in V such that u is visible from v, i.e. the open line segment joining u and v is disjoint from F. An illumination system V is called primitive if no 1 2 Valeriu Soltan, LL aszll ...

We introduce the notion centre of a convex set and study space continuous affine functions on compact with centre. show that these spaces are precisely dual base normed in which underlying has (unique) also characterize corresponding norm space. obtain condition compact, balanced, subset locally space, so is an absolute order unit Similarly, we latter becomes absolutely

for every path a. The corresponding one-shot or stage game is denoted by G = ( {Ai}i=1, { fi}i=1 ) . The usual interpretation is that Ai is a set of pure actions.1 The set of feasible payoff vectors of the stage game G is given by the set F ≡ {p ∈ Rn| f (a) = p for some a ∈ A}. Let F∗ be the convex hull of the set of feasible payoffs. It should be clear that any normalized payoff in the repeate...

In the eld of nonlinear programming (in continuous variables) convex analysis [21, 22] plays a pivotal role both in theory and in practice. An analogous theory for discrete optimization (nonlinear integer programming), called \discrete convex analysis" [18, 17], is developed for L-convex and M-convex functions by adapting the ideas in convex analysis and generalizing the results in matroid theo...