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

By Shigeo Kusuoka, Toru Maruyama

The sequence is designed to collect 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 study. loads of financial difficulties may be formulated as restricted optimizations and equilibration in their recommendations. a number of mathematical theories were delivering economists with critical machineries for those difficulties coming up in fiscal idea. Conversely, mathematicians were encouraged through a variety of mathematical problems raised through monetary theories.

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Let xn 2 Y with xn ! Œ0; 1/. 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.

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 . 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 !

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.

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