Sequences of contractive maps and fixed points

Robert Fraser and Sam Bernard Nadler, Jr.

Vol. 31 (1969), No. 3, 659–667

DOI: 10.2140/pjm.1969.31.659

Abstract

Let (X,ρ₀) be a metric space and, for each n = 0,1,2,⋯ , let f_n : X → X be a function with fixed point a_n. Assume that each function f_n is contractive with respect to a (possibly) different metric ρ_n, where each ρ_n is equivalent to ρ₀. This paper is concerned with the behavior of the sequence {a_n}_n=1^∞ when {f_n}_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