Quickies
88 Citations•2015•
N. Stanciu, G. Palade
Mathematics Magazine
No TL;DR found
Abstract
Answers to the Quickies are on page 78. Q1047. Proposed by Michael W. Botsko, Saint Vincent College, Latrobe, PA. Let (X, d) be a complete metric space and let f : X → X . Suppose there exists r > 1 such that d( f (x1), f (x2)) ≥ r · d(x1, x2) for all x1 and x2 in X . (a) Prove that if f is onto, then f has a unique fixed point in X . (b) Is the conclusion in part (a) still true without the assumption that f is onto?