Fixed Point Theorem of Nonexpansive Mappings in Convex Metric Spaces

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Li Bing-you. Fixed Point Theorem of Nonexpansive Mappings in Convex Metric Spaces[J]. Applied Mathematics and Mechanics, 1989, 10(2): 173-178.

Citation:

Li Bing-you. Fixed Point Theorem of Nonexpansive Mappings in Convex Metric Spaces[J]. Applied Mathematics and Mechanics, 1989, 10(2): 173-178.

Citation:

Li Bing-you. Fixed Point Theorem of Nonexpansive Mappings in Convex Metric Spaces[J]. Applied Mathematics and Mechanics, 1989, 10(2): 173-178.

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,y)+b{d(x,Tx)+d(y,Ty)}+c{d(x,Ty)+d(y,Tx)},∀x,y∈K
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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