FIXED POINT THEOREM OF NONEXPANSIVE MAPPINGS IN CONVEX METRIC SPACES

<正> Let X be a convex metric space with the property that every decreasing sequence ofnonempty closed subsets of X with diameters tending to(?)has nonempty intersection.This paper proved that if T is a mapping of a closed convex nonempty subset K of X intoitself satisfying the inequality:d(Tx,ty)≤ad(x.y)+b{d(x,Tx)+d(y,Ty}+c{d(x,Ty)+d(y,Tx)}for allλ.yin K,where0≤a<1,b≥0,c≥0,a+c≠0 and a+2b+3c≤1,then T has auniquc fixed point in K.