Bulletin of the Australian Mathematical Society

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A VARIATION ON THE THEME OF NICOMACHUS
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FLORIAN LUCA, GEREMÍAS POLANCO, WADIM ZUDILIN
Published online by Cambridge University Press:

28 March 2018, pp. 367-373
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In this paper, we prove some conjectures of K. Stolarsky concerning the first and third moments of the Beatty sequences with the golden section and its square.

The Krasnosel’skiĭ–Mann (KM) iteration is a widely used method to solve fixed point problems. This paper investigates the convergence rate for the KM iteration. We first establish a new convergence rate for the KM iteration which improves the known big- $O$ rate to little- $o$ without any other restrictions. The proof relies on the connection between the KM iteration and a useful technique on the convergence rate of summable sequences. Then we apply the result to give new results on convergence rates for the proximal point algorithm and the Douglas–Rachford method.

FRACTIONAL MODELS IN SPACE FOR DIFFUSIVE PROCESSES IN HETEROGENEOUS MEDIA WITH APPLICATIONS IN CELL MOTILITY AND ELECTRICAL SIGNAL PROPAGATION
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NICOLE CUSIMANO
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10 February 2016, pp. 518-520
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ORBITALLY NONEXPANSIVE MAPPINGS
Part of:
- Smooth dynamical systems: general theory
- Nonlinear operators and their properties
ENRIQUE LLORENS-FUSTER
Published online by Cambridge University Press:

11 November 2015, pp. 497-503
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We define a class of nonlinear mappings which is properly larger than the class of nonexpansive mappings. We also give a fixed point theorem for this new class of mappings.

Bulletin of the Australian Mathematical Society

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A VARIATION ON THE THEME OF NICOMACHUS

ON THE CONVERGENCE RATE OF THE KRASNOSEL’SKIĬ–MANN ITERATION

Abstracts of Australasian PhD Theses

FRACTIONAL MODELS IN SPACE FOR DIFFUSIVE PROCESSES IN HETEROGENEOUS MEDIA WITH APPLICATIONS IN CELL MOTILITY AND ELECTRICAL SIGNAL PROPAGATION

Research Article

ORBITALLY NONEXPANSIVE MAPPINGS

Bulletin of the Australian Mathematical Society

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Open access

Research Article

A VARIATION ON THE THEME OF NICOMACHUS

ON THE CONVERGENCE RATE OF THE KRASNOSEL’SKIĬ–MANN ITERATION

Abstracts of Australasian PhD Theses

FRACTIONAL MODELS IN SPACE FOR DIFFUSIVE PROCESSES IN HETEROGENEOUS MEDIA WITH APPLICATIONS IN CELL MOTILITY AND ELECTRICAL SIGNAL PROPAGATION

Research Article

ORBITALLY NONEXPANSIVE MAPPINGS