Vol. 48, No. 1, 1973

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Common fixed points of two mappings

Chi Song Wong

Vol. 48 (1973), No. 1, 299–312
Abstract

Let S,T be functions on a nonempty complete metric space (X,d). The main result of this paper is the following. S or T has a fixed point if there exist decreasing functions α12s45 of (0,) into [0,1) such that (a) Σi=16αi < 1; (b) α1 = α2 or α8 = α4, (c) limt0(α1 + α2) < 1 and limt0(α8 + α4) < 1 and (d) for any distinct x,y in X,

d(S(x),T(y)) a1d(x,S(x)) + a2d(y,T(y)) + a3d(x,T(y))
+ a4d(y,S(x)) + a5d(x,y),
where ai = αi(d(x,y)). A number of related results are obtained.

Mathematical Subject Classification 2000
Primary: 54H25
Milestones
Received: 13 June 1972
Published: 1 September 1973
Authors
Chi Song Wong