About the Mahony Neumann Room Prize

This prize, for outstanding contributions to the Australian Mathematical Society’s research publications, is fittingly named after the founding editors of those journals. The people it honours represent the three major aspects in the development of Australian mathematics.

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Winner of the 2020 Mahony Neumann Room Prize

Australian Mathematical Society (AustMS) has awarded the 2020 Prize to Janusz Brzdek for the paper “A Hyperstability Result for the Cauchy Equation”, Bulletin of the Australian Mathematical Society.

Citation: The paper proves a hyperstability result for the Cauchy functional equation f(x + y) = f(x) + f(y), which complements earlier stability outcomes of J. M. Rassias. It exploits the fixed point method introduced in J. Brzdęk, J. Chudziak and Zs. Páles, ‘A fixed point approach to stability of functional equations’, Nonlinear Anal. 74 (2011), 6728–6732. The notion of hyperstability for this functional equation (also introduced by J. Brzdęk) is that if a mapping is in some sense ‘close’ to being additive, is it necessarily ‘close’ to an additive mapping.

The methods introduced in the paper are presented in a form that has been shown to be widely applicable and has influenced others working in this field with applications to many other functional equations and in more general settings. The fixed point method from Brzdęk, Chudziak and Páles has also been developed in many papers to a number of functional equations and to a number of settings beyond the original setting in Banach space and the application to the Cauchy equation.

This paper continues to be strongly cited as one of a growing number of examples of hyperstability, acknowledging the significance of the early application of the method to the Cauchy equation.

The winning paper, as well as all the shortlisted papers, will be available to read for free through 2021.

Click here to see view the shortlisted papers.