Download Advances in Mathematical Economics, Vol. 10 by S. Kusuoka, A. Yamazaki PDF

By S. Kusuoka, A. Yamazaki

ISBN-10: 4431727337

ISBN-13: 9784431727330

Published every year lower than the auspices of the study heart of Mathematical Economics in Tokyo, this sequence brings jointly mathematicians attracted to financial theories and economists looking potent mathematical instruments to assist their examine. Articles set forth unique effects and targeted overviews of the issues below dialogue, supplying readers a transparent knowing of either monetary and mathematical theories.

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Ibaraki and W. Takahashi We know that the duality mappings J oniP, \ < p < cx) and smooth finite dimensional Banach spaces are weakly sequentially continuous. 2 hold without assuming that J is weakly sequentially continuous. 4. Strong convergence theorem Let £• be a reflexive, strictly convex, and smooth Banach space and let J be the duahty mapping from E into £"*. Then J~^ is also single valued, one-to-one, and surjective, and it is the duaUty mapping from E* into E. 1) for 2i\lx e E and jc* e E*.

Under Assumption 1, there is a po € (—1,0) such thatfor any given Po > Po there exists p\ e [pi, 0) such that g(p\) is a monotone increasing function for all pi > p\. Proof Notice first that api\i + pi/ (i + P i ) ^ ' ' ' a p i \ PPi(l i ( i + Po)/ PO Pf(l + Po) It follows that for any given po > 0, g(p\) is a monotone increasing function when p\ > 0. Consider now the case po e (~1,0). We can write g{p\) as follows: g(p\) = exp Pi - Po , ^^^p[Tfk^-(fe)]-^^i -In Pi(l + Po) I Po\ = exp{/(pi)}. Capital-labor substitution and indeterminacy 45 If / ( p i ) is monotone increasing, so is g(p\).

Econ. 1, 17-37 (1999) 15. : Tightness conditions and Integrability of the sequential weak upper limit of a sequence of Multifunctions. Working paper 2005 16. : On various versions of Fatou lemma. Working paper 2006 17. : Dunford-Pettis-types theorem and convergences in set-valued integration, J. Nonlinear Convex Anal. 1(1), 37-71 (2000) 18. : Convex Analysis and Measurable Multifunctions, Lectures Notes in Mathematics, Springer, Berlin, 580, 1977 19. : Subsequence principles for vector-valued random variables.

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