Advances in Mathematical Economics Volume 20 by Shigeo Kusuoka, Toru Maruyama

By Shigeo Kusuoka, Toru Maruyama

The sequence is designed to compile these mathematicians who're heavily attracted to getting new hard stimuli from financial theories with these economists who're looking potent mathematical instruments for his or her learn. loads of fiscal difficulties will be formulated as restricted optimizations and equilibration in their recommendations. numerous mathematical theories were providing economists with crucial machineries for those difficulties bobbing up in fiscal thought. Conversely, mathematicians were prompted by way of quite a few mathematical problems raised by means of monetary theories.

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36 C. Castaing et al. 2. Let X W Œ0; 1 ,! E be a convex weakly compact valued measurable and integrably bounded mapping. Let F W Œ0; 1 E E ,! t; x; y/ 2 Œ0; 1 E E. Œ0; 1/. Proof. h/ SX1 . t//, t 2 Œ0; 1. Œ0; 1/-solution 1 1 1 1 to (17). We show that ˆ W SX ,! LE ; LE /-compact valued upper semicontinuous mapping. L1E ; L1 E /-closed. L1E ; L1 E /-converges to h 2 SX and . fn / E /-converges to f 2 SX . h/. t/ ! t/ ! t/ for each t 2 Œ0; 1, for E endowed with the weak topology. E/: On a Fractional Differential Inclusion in Banach Space Under Weak.

S//jds: 40 C. Castaing et al. ˛/ 1 jhx ; uf . Œ0; 1/. s/ ds. Œ0; 1/. Let . fn / be a sequence in S€Pe . We note that SXPe is sequentially compact for the topology of pointwise convergence on L1 ˝ E . Œ0; 1/. Indeed we can extract from . fn / a sequence . fm / such that . P1E ; L1 ˝ E /-converges to a function f 2 SXPe . Œ0; 1/ to uf . Œ0; 1/. P1E ; L1 ˝ E /-convergence of . 5(iv). Remark. 2, we have proven the continuous dependence of the mappings f 7! uf and f 7! P1E ; L1 ˝ E /-compact set SXPe .

1. L derivatives of ˛ and ˛ 1 respectively, F is a convex compact valued upper semi continuous mapping. L derivatives of ˛ and ˛ 1 respectively, F is a convex weakly compact valued mapping. We need at first some Pettis analogs of the results developed in the preceding section. 1. Œ0; 1/ be a Pettis-integrable function. s/ds; t 2 Œ0; 1 On a Fractional Differential Inclusion in Banach Space Under Weak. . t/dt We begin with a crucial lemma. 2. Let X W Œ0; 1 ,! Œ0; 1/-solutions set X to the (FDI) integrable multifunction.

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