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A Cosine Functional Equation with Restricted Argument

Published online by Cambridge University Press:  20 November 2018

L. B. Etigson
L. B. Etigson*
Affiliation:
Department of Mathematics, Atkinson College, York University, Downs View, Ontario
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We name a functional equation with restricted argument one in which at least one of the variables is restricted to a certain discrete subset of the domain of the other variable(s). In particular, the subset may consist of a single element.

The purpose of this paper is to present a functional equation satisfied only by cosine functions.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 4 , 01 December 1974 , pp. 505 - 509
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Aczel, J., Lectures on functional equations and their applications, Academic Press, New York and London, 1966.Google Scholar
2. Kaczmarz, S., Sur l'equation fonctionelle f(x)+f(x+y)=ϕ(y)f[x+(y/2)], Fund. Math. 6 (1924), 122-129.Google Scholar
3. Kannappan, Pl., A functional equation for the cosine, Canad. Math. Bull. 2 (1968), 495-498.Google Scholar
4. Kannappan, Pl., The functional equation f(xy)+f(xy-1)=2f(x)f(y) for groups, Proc. Am. Math. Soc. 19 (1968), 69-74.Google Scholar
5. Kannappan, Pl., On sine functional equation, Stud. Sci. Math. Hung. 4 (1969), 331-333.Google Scholar
6. Van Vleck, B., Afunctional equation for the sine, Ann. Math. 7 (1910), 161-165.Google Scholar
7. Wilson, W. H., On certain related functional equations, Bull. Am. Math. Soc. 26 (1918), 300-312.Google Scholar