By Houcine Benabdellah, Charles Castaing (auth.), Shigeo Kusuoka, Toru Maruyama (eds.)

ISBN-10: 4431659374

ISBN-13: 9784431659372

ISBN-10: 4431678913

ISBN-13: 9784431678915

Loads of monetary difficulties can formulated as restricted optimizations and equilibration in their suggestions. quite a few mathematical theories were providing economists with integral machineries for those difficulties coming up in monetary concept. Conversely, mathematicians were inspired through a number of mathematical problems raised by way of monetary theories. The sequence is designed to collect these mathematicians who have been heavily attracted to getting new tough stimuli from financial theories with these economists who're looking for potent mathematical instruments for his or her researchers. individuals of the editorial board of this sequence comprises following popular economists and mathematicians: handling Editors: S. Kusuoka (Univ. Tokyo), T. Maruyama (Keio Univ.) Editors: R. Anderson (U.C.Berkeley), C. Castaing (Univ. Montpellier), F. H. Clarke (Univ. Lyon I), G. Debreu (U.C. Berkeleyer), E. Dierker (Univ. Vienna), D. Duffie (Stanford Univ.), L.C. Evans (U.C. Berkeley), T. Fujimoto (Okayama Univ.), J. -M. Grandmont (CREST-CNRS), N. Hirano (Yokohama nationwide Univ.), L. Hurwicz (Univ. of Minnesota), T. Ichiishi (Ohio kingdom Univ.), A. Ioffe (Israel Institute of Technology), S. Iwamoto (Kyushu Univ.), okay. Kamiya (Univ. Tokyo), ok. Kawamata (Keio Univ.), N. Kikuchi (Keio Univ.), H. Matano (Univ. Tokyo), okay. Nishimura (Kyoto Univ.), M. ok. Richter (Univ. Minnesota), Y. Takahashi (Kyoto Univ.), M. Valadier (Univ. Montpellier II), M. Yano (Keio Univ).

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Workshop di Teoria della Misura e Analisi Reale, Grado, September 19-0ctober 2 (1993). Rend. Matematica Trieste suppl. (26), 349-394 (1994) 44 H. Benabdellah, C. : Strong convergence results related to strict convexity. Comment. Partial Diff. : Equilibria in Non-cooperative Models of Competition. J. Economic. Theory. : Fatou's lemma in Infinite Dimensional spaces. Proc. Amer. Math . Soc. 1988 Adv. Math. Econ. D. il) Received: September 7, 2000 Revised: November 29, 2000 JEL classification: C61 Mathematics Subject Classification (2000): 49J52, 90C48 1.

Clearly, cp is a continuous function on X x H if every element of H is a continuous function and the convergence in H implies uniform convergence in a neighborhood of any x EX. Definition 1. An extended-real-valued function f on X is called w-convex if f(x) = sup{w(x, h) + c: c E JR, w(u, h) + c::; f(u), VuE X}. Likewise, an extended real-valued function 9 on H is w-convex if g(h) = sup{w(x, h) + c: c E JR, w(x, k) + c::; g(k), V k E H}. Clearly, any w-convex function is lower semi-continuous. If we adopt the standard convention that sup 0 = -00, then we conclude from the definition that any w-convex function is either identically equal to minus infinity or is greater than -00 at every point.

1 the sequence (v n ) is relatively sequentially 0"(L1, [E], (L1, [E])') compact. By extracting an appropriate subsequence, we may suppose that (v n ) converges to v E L1, [E] for this topology. It follows that (w n ) weakly converges to -v. e and Un weakly converges to 0, we get v = 0. e. Hence t/. e. ). ) \BE,(O,E) from ° t ° ° The measurability of {w EO: un{w) (j. BE,{O,c)} will be demonstrated later. ), too. ). Hence the multifunction W defined on A with nonempty values in the closed unit ball BE of E (thanks to Hahn-Banach's theorem) : w(w) = {x E BE: 8*(x, ~(w)) < O} has its graph in An F 0 B(BE).

### Advances in Mathematical Economics by Houcine Benabdellah, Charles Castaing (auth.), Shigeo Kusuoka, Toru Maruyama (eds.)

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