Restricted Oriented Slack Convexity and Extremal Elements with Respect to a Set

In a real linear space V , a set of directions O ⊂ V and a set of representative vectors M ⊂ V generate a double re- stricted concept of convexity: with directional and with particular punctual restrictions. A Krein-Milman type property for slack O- directionally convex sets with respect to M is derived in terms of double restricted extremal elements of a set.