Vol. 31, No. 3, 1969

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Sequences of contractive maps and fixed points

Robert Fraser and Sam Bernard Nadler, Jr.

Vol. 31 (1969), No. 3, 659–667
Abstract

Let (X,ρ0) be a metric space and, for each n = 0,1,2, , let fn : X X be a function with fixed point an. Assume that each function fn is contractive with respect to a (possibly) different metric ρn, where each ρn is equivalent to ρ0. This paper is concerned with the behavior of the sequence {an}n=1 when {fn}n=1 converges pointwise to f0.

Mathematical Subject Classification
Primary: 54.85
Milestones
Received: 22 January 1969
Revised: 23 April 1969
Published: 1 December 1969
Authors
Robert Fraser
Sam Bernard Nadler, Jr.