Vol. 82, No. 2, 1979

Recent Issues
Vol. 329: 1
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Online Archive
The Journal
About the journal
Ethics and policies
Peer-review process
Submission guidelines
Submission form
Editorial board
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author index
To appear
Other MSP journals
General Pexider equations. II. An application of the theory of webs

M. A. McKiernan

Vol. 82 (1979), No. 2, 503–514

Given open connected Ω, Ω Rn and continuous T : Ω R, F : Ω R both strictly monotonic in each variable separately. The equation h{T(x1,,xn)} = F{f1(x1),,fn(xn)} for the unknowns h : T(Ω) R and π : (f1,,fn) : Ω Ω can be interpreted within the theory of webs (the “Gewebe” of Blaschke-Bol). The web structure is then used to prove: any continuous solution π is uniquely determined on Ω by its value at two points of Ω; if a solution π is not continuous on Ω, then π(ω) is dense in Ω for every open ω in Ω; if a solution π is continuous at one point of Ω, it is continuous on Ω.

Mathematical Subject Classification
Primary: 39B20, 39B20
Secondary: 39B50
Received: 13 March 1978
Revised: 20 October 1978
Published: 1 June 1979
M. A. McKiernan
Department of Mathematics
University of Waterloo
Waterloo ON N2L 3G1