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 hard stimuli from monetary theories with these economists who're looking powerful mathematical instruments for his or her study. loads of fiscal difficulties might be formulated as limited optimizations and equilibration in their ideas. a variety of mathematical theories were delivering economists with integral machineries for those difficulties bobbing up in fiscal idea. Conversely, mathematicians were influenced through numerous mathematical problems raised by means of monetary theories.

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Un / such that un ! u and vn ! v in X . t/ ! t/ ! t/ ! t/ ! Œ0; 1; dt/ and x 2 E . t/// a:e: On a Fractional Differential Inclusion in Banach Space Under Weak. . t/// a:e: By virtue of ([17], Prop. t// a:e: thus proving that the graph of ˆ is weakly compact in X X. We finish this section by providing some new variants of the above stated theorems. The following lemma is useful for our purpose. 3. Œ0; 1/. Then the mapping uf W Œ0; 1 ! 0/ D b: Proof. 0/ D 0. ˛/ 1 From the classical calculus of fractional order integral and R.

0; 1/. t/: On a Fractional Differential Inclusion in Banach Space Under Weak. . t/: Remark. 4, we have proven the continuous dependence of the mappings f 7! uf and f 7! L1E ; L1 E /compact set SX1 . This fact has some importance in further applications. 2. Let X W Œ0; 1 ,! E be a convex compact valued measurable and integrably bounded mapping. Let F W Œ0; 1 E E ,! t; x; y/ 2 Œ0; 1 E E. Œ0; 1/ endowed with the topology of uniform convergence. Proof. h/ SX1 . t//, t 2 Œ0; 1. Œ0; 1/-solution to (24).

Uf and f 7! P1E ; L1 ˝ E /-compact set SXPe . This fact has some importance in further applications. On a Fractional Differential Inclusion in Banach Space Under Weak. . s/ds: is weakly compact in E. 1. Let X W Œ0; 1 ,! E be a convex weakly compact valued Pettisintegrable multifunction. Let F W Œ0; 1 E E ,! t; x; y/ 2 Œ0; 1 E E. Œ0; 1/. Proof. Taking the above stated results into account, a mapping u W Œ0; 1 ! 2. t/ a:e:g: 42 C. Castaing et al. u/ is nonempty, convex weakly compact in X .

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