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A result concerning additive maps on the set of quaternions and an application

Published online by Cambridge University Press:  17 April 2009

Damjan Kobal  and
Peter Šemrl
Damjan Kobal
Affiliation:
Department of Mathematics, University of Ljubljana, Jadranska 19 61000 Ljubljana, Yugoslavia
Peter Šemrl
Affiliation:
Department of Mathematics, University of Ljubljana, Jadranska 19 61000 Ljubljana, Yugoslavia
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Abstract

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We determine all additive F, G: ℍ → ℝ and multiplicative M: H → ℝ satisfying the functional equation F(λ) + M(λ)G(λ−1) = 0. As an application we generalise Kurepa's solution of one of Halperin's problem concerning quadratic functionals.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 44 , Issue 3 , December 1991 , pp. 477 - 482
Copyright
Copyright © Australian Mathematical Society 1991

References

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