By Guillaume Carlier (auth.), Shigeo Kusuoka, Toru Maruyama (eds.)

**Research Articles**: G. Carlier, Duality and lifestyles for a category of mass transportation difficulties and fiscal functions; Charles Castaing and Ahmed Gamal Ibrahim: practical evolution equations ruled by means of m-accretive operators; Leonid Hurwcz and Marcel ok. Richter, Implicit services and diffeomorphisms with no C; Leonid Hurwicz and Marcel ok. Richter, Optimization and Lagrange multipliers: Non-C1 Constraints and minimum constraint skills; Takao Fujimoto, Jose A. Silva and Antonio Villar, Nonlinear generalizations of theorems on inverse-positive matrices; Shigeo Kusuoka, Monte Carlo strategy for pricing of Bermuda sort derivatives.- **Historical Perspectives**: Isao Mutoh, Mathematical economics in Vienna among the wars.- topic index.

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**Extra info for Advances in Mathematical Economics**

**Example text**

A(k x) = kA( x) forany positive scalark. 2*. 2*. , then x » O. 3 are satisfied. First we present 60 T. Fujimoto, JA Silva, A. 1. 3, there exists a A* such that (i) if A > A*, T(x ; A) = d has a unique solution x » 0 for any d > 0, and (ii) T(x ; A*) = 0 has a nonzero solution x* » 0, which is unique up to scalar multiplication. Proof. These are the results contained in Morishima and Fujimoto[7] and Fujimoto[4], thus the proof is omitted. 2. 4. 1. 2* does not hold for - T( x ; A) in any interval like A° < A < A*.

Here JA(t) stands for JAA(t). 5) 2 ::; 2(A nAAn(t)UAn(t) - AmAA m(t)U Am(t) , uAJt) - UAm(t) ) = -2 (A nUAn(t) - AmU Am(t) ,UAn(t) - UAm(t) ). ) - u Am( ') ) (L~{([O ,tJ) ,L~([O ,t])) ::; o. 7) and [11], (u,XJ)) converges in the Hilbert space LJI([O ,I]) . Let v be the limit of (u,XJ)) and let, for all t E [0, 1] u(t) = a + l t v(s ) ds. ) in CH([O , 1]) becau se the mapping f t-4 Jo f( s) ds from LJI([O, 1]) to Cu([O, 1]) is continuous for the norm topologies. e t E [0,1], { u(O) = a E H. 10) = AnIIA,X" (t )u,X" (t)11 = Anllu'x" (t)11 :S Anß(t).

So, taking Functional evolution equations govemed by m-accretive operators 33 d(- un(t ) + gn(t) , A(t)wn (t )) = d (U n(8n(t )) - un((}n (t)) + gn(t ), A(t)Wn(t) ) en 1 S; -llun((}n(t)) - wn(t) 11 en S; IP((}n (t)) - p(t )IL(ß + IKI). e with rn(t) := IP((}n (t)) - p(t)IL (ß + IKI) ~ for an t E [0,1] . e i t E [0,1] . « [0,1]. Let tE [0, 1]. 9) we get II T(8n(t ))un - T(t)u IICE([-r,OJ) S; IIT(8n(t))un - T(t)u nIICE([-r,OJ) + IIT(t)Un - T(t)uIICE([- r,OJ) S; sup Ilun(Sl) - un(s2) 11+ IIT(t)Un - T(t)uIICE([-r,OJ) {S I ,S2E[- r ,l]' ls 1 -S2 1