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Applied Mathematics and Mechanics (English Edition) ›› 1989, Vol. 10 ›› Issue (2): 183-188.

• 论文 • 上一篇    下一篇

FIXED POINT THEOREM OF NONEXPANSIVE MAPPINGS IN CONVEX METRIC SPACES

李秉友   

  1. Department of Mathematics, Hebei Normal University, Shijiazhuang
  • 收稿日期:1987-10-24 出版日期:1989-02-18 发布日期:1989-02-18

FIXED POINT THEOREM OF NONEXPANSIVE MAPPINGS IN CONVEX METRIC SPACES

Li Bing-you   

  1. Department of Mathematics, Hebei Normal University, Shijiazhuang
  • Received:1987-10-24 Online:1989-02-18 Published:1989-02-18

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摘要： Let X be a convex metric space with the property that every decreasing sequence of nonenply dosed subsets of X with diameters tending to has menemptyintersection. This paper proved that if T is a mapping of a elosed conver nonempty subset K of X into itself satisfying the inequality:
d(Tx,Ty)≤ad(x,t)+b{d(x,Tx)+d(y,Ty)}+c{d(x,Tx)+d(y,Ty)}
for all x,y in K,where 0≤a<1,b≥0,c≥0,a+c≠0 and a+2b+3c≤1, then T has a unique fixed point in K.

Abstract: Let X be a convex metric space with the property that every decreasing sequence of nonenply dosed subsets of X with diameters tending to has menemptyintersection. This paper proved that if T is a mapping of a elosed conver nonempty subset K of X into itself satisfying the inequality:
d(Tx,Ty)≤ad(x,t)+b{d(x,Tx)+d(y,Ty)}+c{d(x,Tx)+d(y,Ty)}
for all x,y in K,where 0≤a<1,b≥0,c≥0,a+c≠0 and a+2b+3c≤1, then T has a unique fixed point in K.

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