Geodesic
The proof of existence of market equilibrium by means of variational inequality
Matematičeskoe modelirovanie, Tome 13 (2001) no. 5, pp. 29-36.

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The duality theorem for generalized programming problems in Banach spaces is proved. The proof of existence of market equilibrium in Arrow–Debreu model is proposed. This proof based on the analysis of variational inequalities. The problem of existence of market equilibrium in the model with transaction costs reduced to the problem of existence of variational inequality solution. 
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     author = {A. A. Shananin},
     title = {The proof of existence of market equilibrium by means of variational inequality},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {29--36},
     publisher = {mathdoc},
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     number = {5},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2001_13_5_a2/}
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A. A. Shananin. The proof of existence of market equilibrium by means of variational inequality. Matematičeskoe modelirovanie, Tome 13 (2001) no. 5, pp. 29-36. http://geodesic.mathdoc.fr/item/MM_2001_13_5_a2/