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Uniqueness theorems for a general class of functional equations

Published online by Cambridge University Press:  09 April 2009

C. T. Ng
C. T. Ng
Affiliation:
University of WaterlooWaterloo, Ontario, Canada
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In a previous paper [1] J. Aczél has shown the followingTheorem 1. If in the (closed, half-closed or open, finite or infinite) interval 〈A, B〉and there f, F are there, f F are continuous, F intern (the value F(x, y) lies strictly between x and y) and u → H(u, v, x, y) or v → H(u, v, x, y) are injective (i.e. or , then the functional equation (*) with the initial conditionshas at most one solution.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 11 , Issue 3 , August 1970 , pp. 362 - 366
Copyright
Copyright © Australian Mathematical Society 1970

References

[1]Aczél, J., ‘Ein Eindeutigkeitssatz in der Theorie der Funktionalgleichungen und einige ihrer Anwendungen’, Acta Math. Acad. Sci. Hung. 15 (1964), 355–362.Google Scholar
[2]Aczél, J. and Hosszú, M., ‘Further Uniqueness Theorems for Functional Equations’, Acta Math. Acad. Sci. Hung. 16 (1965), 51–55.Google Scholar
[3]Aczél, J., ‘On Applications and Theory of Functional Equations’ (Birkhäuser, Basel, 1969, 22–25.Google Scholar
[4]Albrand, Hans-Jürgen, ‘Eindeutigkeitssätze für Funktionalgleichungen’, 1968, Thesis.Google Scholar
[5]Howroyd, T. D., ‘Some Uniqueness Theorems for Functional Equations’, J. Austral. Math. Soc. 9 (1969), 176–179.Google Scholar
[6]Schaefer, H. H., ‘Topological Vector Spaces’, (Macmillan, 1966).Google Scholar