Vol. 82, No. 2, 1979

Recent Issues
Vol. 294: 1
Vol. 293: 1  2
Vol. 292: 1  2
Vol. 291: 1  2
Vol. 290: 1  2
Vol. 289: 1  2
Vol. 288: 1  2
Vol. 287: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
Author Index
To Appear
 
ISSN: 0030-8730
A common fixed point theorem for nested spaces

Raymond Earl Smithson

Vol. 82 (1979), No. 2, 533–537
Abstract

Let X be an arcwise connected Hausdorff space in which the union of any nest of arcs is contained in an arc. Let f,g : X X be commuting functions (not necessarily continuous), which satisfy (1) f(A) and g(A) are arcwise connected for each arc A X, and (2) f1(x) and g1(x) are arcwise connected for each x X. The principal result of this paper is:

Theorem. The functions f and g have a common fixed point.

Mathematical Subject Classification 2000
Primary: 54H25
Milestones
Received: 14 July 1978
Revised: 15 February 1979
Published: 1 June 1979
Authors
Raymond Earl Smithson