By C. Castaing, M. Saadoune (auth.), Shigeo Kusuoka, Akira Yamazaki (eds.)

ISBN-10: 4431727337

ISBN-13: 9784431727330

ISBN-10: 4431727612

ISBN-13: 9784431727613

A lot of financial difficulties can formulated as restricted optimizations and equilibration in their suggestions. a variety of mathematical theories were delivering economists with essential machineries for those difficulties coming up in fiscal idea. Conversely, mathematicians were encouraged by means of quite a few mathematical problems raised through financial theories. The sequence is designed to compile these mathematicians who have been heavily drawn to getting new not easy stimuli from fiscal theories with these economists who're looking for potent mathematical instruments for his or her researchers. contributors of the editorial board of this sequence contains following sought after economists and mathematicians: handling Editors: S. Kusuoka (Univ. Tokyo), A. Yamazaki (Hitotsubashi Univ.) - Editors: R. Anderson (U.C.Berkeley), C. Castaing (Univ. Montpellier II), F. H. Clarke (Univ. Lyon I), E. Dierker (Univ. Vienna), D. Duffie (Stanford Univ.), L.C. Evans (U.C. Berkeley), T. Fujimoto (Fukuoka Univ.), J. -M. Grandmont (CREST-CNRS), N. Hirano (Yokohama nationwide Univ.), L. Hurwicz (Univ. of Minnesota), T. Ichiishi (Hitotsubashi Univ.), A. Ioffe (Israel Institute of Technology), S. Iwamoto (Kyushu Univ.), okay. Kamiya (Univ. Tokyo), ok. Kawamata (Keio Univ.), N. Kikuchi (Keio Univ.), T. Maruyama (Keio Univ.), H. Matano (Univ. Tokyo), ok. 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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Anal. 117, 167-191 (1992) Komlos type convergence with applications 29 2. : New fundamentals of Young measure convergence. In: Calculus of variations and optimal control, Haifa (1998), Chapman Hall, Boca Raton 24-48 (2000) 3. : A general approach to lower semicontinuity result and lower closure in optimal control theory. SIAM J. Control Optim. 22, 570-598 (1984) 4. : Two generalizations of Komlos theorem with lower closuretype aplications. J. Convex Anal. 3, 25-44 (1996) 5. , Castaing, C: Weak compactness and convergences in L^,[£'].

4) that V(Xn-^\,Rx) = V\(Xn+\,JRx) = < Vi(anx + (1 - an)yn, JRx) V\{anX + (1 - an)yn - oin(x - Rx), JRx) — 2{—an(x — Rx), Jxn-\-\ — JRx) = Vi(anRx + {l-an)yn,JRx) ~\-2an{x — Rx, JXn-\-\ — JRx) < V(anRx + (1 - an)yn, Rx) + 2anS < anV{Rx, Rx) + (1 - an)V(yn, Rx) + 2anS. 1, we have V(jc„+i, Rx) < = (1 - an)V(Xn, Rx) + 2ane 26{l-(l-an)} + {l-an)V{xn,Rx). Rx) for all n >m. Since YA^\ ^i — ^ ' ^ ^ ^^^^ D/Sm (^ - a/) = 0 (see Takahashi [21]). Hence, we have limsupy(x„, Rx) = lim sup V(Xfn-\-i-\-\, Rx) < lim sup 2e m-\-l m+l l-[](l-a/) + Yl{l-ai)V{x,n,Rx) = 2e.

Z) being the compact metrizable space of all probability Radon measures defined on Z, endowed with the vague topology and let Hbe a convex weakly compact subset 6>/L^([0, 1], dt). Let us consider the integral fiinctional J{u, k) := \ Jo Uz j(t, u(t), z)Xt(dz) dt; J V(M, k) eHxIZ. Then the following hold: (a) there is a pair (u,X) eH x7Z such that maxmin/(M, X) < J(u, X) < XeTlueH vmnm3xJ(u,X). ueH veU (b) max min J(u, k) = min max 7(M, k). Proof (a) follows the same line of the proof of the preceding result.

### Advances in Mathematical Economics by C. Castaing, M. Saadoune (auth.), Shigeo Kusuoka, Akira Yamazaki (eds.)

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