To deal with the feature extraction difficulty caused by figure stroke break or stroke fusion in image recognition, a method based on coupling end-point direction is put forward to repair the broken stroke.

Theorems of coupled fixed point and its iteration of mixed monotone maps;

By using point valued method for set-valued mappings in Hilbert space,coupled fixed points theorem for asymptotically nonexpansive mappings of semi-compact and noncontinous binary set-valued and convergence of iterative sequence are obtained.

In strictly convex Banach space,there is set F(T) of coupled fixed points of T for nonexpansive mapping,and it is a closed convex set.

The couple fixed point of set-valued nonexpansive mappings in hilbert space;

The existence and approximations theorem for approximations couple fixed point of semi compact nonexpansive mappings;

The existence of the couple fixed points of a discontinuous mixed monotone multifunction is discussed,and the form of the couple fixed point is also given.

Separating coupling node area from distribution network based on adjacency matrix;