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

By Shigeo Kusuoka, Toru Maruyama

The sequence is designed to compile these mathematicians who're heavily attracted to getting new not easy stimuli from fiscal theories with these economists who're looking potent mathematical instruments for his or her study. loads of fiscal difficulties might be formulated as restricted optimizations and equilibration in their recommendations. a variety of mathematical theories were delivering economists with imperative machineries for those difficulties bobbing up in monetary thought. Conversely, mathematicians were influenced via quite a few mathematical problems raised by means of financial theories.

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Advances in Mathematical Economics Volume 20

The sequence is designed to assemble these mathematicians who're heavily drawn to getting new hard stimuli from fiscal theories with these economists who're looking powerful mathematical instruments for his or her learn. loads of financial difficulties might be formulated as limited optimizations and equilibration in their suggestions.

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T/ ! t/ weakly in E for each t 2 Œ0; 1. t// ! t// weakly in E for each t 2 Œ0; 1. ://. s//ids n A A A using (iii). s//i a:e: for each x 2 E . e. s//ds ! Œ0; 1/ showing that ˆ W Y ! Y is continuous on the convex weakly compact Y. x/ that constitutes a solution of the integral equation under consideration. In the vein of the above result, we provide a fairly general existence theorem in multivalued Pettis integral inclusion which has an independent interest and which leads to the existence of solutions for some differential inclusion and fractional differential inclusion with boundary conditions in the Pettis setting.

Proof. See Grothendiek ([29], page 296). 2. Œ0; 1/. 1 and the measure of weak noncompactness [5, 24]. g. 8 in [34]. L derivatives of order ˛ and ˛ 1 respectively, F is a convex weakly compact valued mapping. Here we consider at first the Bochner case. 2, we have the following result. 3. Œ0; 1/ be a Bochner-integrable function. t/dt 34 C. Castaing et al. This result is useful in establishing the study of the fractional differential inclusion (FDI). 1. Let X W Œ0; 1 ,! Œ0; 1//. Œ0; 1/. Œ0; 1/-solutions set X to (16) is characProof.

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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