## Advances in Mathematical Economics, Volume 15Shigeo Kusuoka, Toru Maruyama A lot of economic problems can be formulated as constrained optimizations and equilibration of their solutions. Various mathematical theories have been supplying economists with indispensable machineries for these problems arising in economic theory. Conversely, mathematicians have been stimulated by various mathematical difficulties raised by economic theories. The series is designed to bring together those mathematicians who are seriously interested in getting new challenging stimuli from economic theories with those economists who are seeking effective mathematical tools for their research. |

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### Contents

1 | |

A note on robust representations of lawinvariant quasiconvex functions | 27 |

On the Fourier analysis approach to the Hopf bifurcation theorem | 41 |

Fixed point theorems and ergodic theorems for nonlinear mappings in Banach spaces | 66 |

On the perception and representation of economic quantity in the history of economic analysis in view of the Debreu conjecture | 89 |

An existence result and a characterization of the least concave utility of homothetic preferences | 123 |

129 | |

Instructions for Authors | 133 |

### Other editions - View all

Advances in Mathematical Economics, Volume 16 Shigeo Kusuoka,Toru Maruyama No preview available - 2012 |

Advances in Mathematical Economics, Volume 15 Shigeo Kusuoka,Toru Maruyama No preview available - 2013 |

### Common terms and phrases

a e Q analysis Assumption B-measurable closed convex subset commodity space concave utility function conditional expectation continuous convex Banach space Cournot Debreu conjecture demand curve denote differentiable discontinuity of individual economic quantities equilibrium ergodic theorem exists Fixed point theorems Fourier coefficients Gâteaux differentiable Hilbert space Hopf bifurcation theorem Ibaraki indifference curves individual demand functions indivisible commodity integrable io"I Kohsaka Kusuoka large numbers law of large law-invariant least concave utility Lemma lower semicontinuous Marshall martingales Maruyama Math monotone multifunctions n-co negligible set nonempty closed convex nonexpansive mapping nonexpansive retraction nonspreading mapping normal integrands Pareto preference relation probability space Proof q_x(t real numbers resp result risk measures RT"x satisfying separable Banach space sequence space and let step curve sub-o-algebra sunny generalized nonexpansive superadditive Takahashi topological total demand u e F(T upper hemi-continuous utility function variations Walras weak convergence