Vol. 82, No. 2, 1979

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General Pexider equations. I. Existence of injective solutions

M. A. McKiernan

Vol. 82 (1979), No. 2, 499–502
Abstract

Given open connected Ω, Ω Rn and given T : Ω R continuous, F : Ω R strictly monotonic, in each variable separately. The equation is h T = F π for the unknowns h : T(Ω) R, π : Ω Ω with π = (f1,,fn) a product mapping - e.g., h{T(x,y)} = F{f(x),g(y)}. If T is one-one in each variable, then any continuous solution π must be injective or constant on Ω; conversely, if an injective solution π exists then T must be one-one in each variable separately.

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