Vol. 54, No. 1, 1974

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Fixed points and characterizations of certain maps

Chi Song Wong

Vol. 54 (1974), No. 1, 305–312
Abstract

Let T be a self map on a metric space (X, d) such that

d(T (x ),T(y)) ≦ (d(x,T(x))+ d(y,T (y)))∕2, x,y ∈ X.

It is proved that: (a) T has a fixed point if T is continuous and X is weakly compact convex subset of a Banach space. (b) All such T which have fixed points can be explicitly determined in terms of d. Related results are obtained.

Mathematical Subject Classification 2000
Primary: 47H10
Milestones
Received: 28 March 1973
Published: 1 September 1974
Authors
Chi Song Wong