This article is cited in 3 papers

Polyhedral complementarity on a simplex. Potentiality of regular mappings

V. I. Shmyrev<sup>ab

a</sup> Sobolev Institute of Mathematics SB RAS, 4 Koptyug av., 630090 Novosibirsk
^b Novosibirsk State University, 2 Pirogova str., 630090 Novosibirsk

Abstract: We consider a special class of the fixed point problems for piecewise constant mappings of a simplex into itself. These are polyhedral complementarity problems arising in studying the classical exchange model and its variations. We study the problems that stem from the consideration of models with fixed budgets and possessing a certain property of monotonicity (logarithmic monotonicity). Our considerations are purely mathematical and not associated with the economic models that gave rise to these mathematical objects. The class of regular mappings is investigated, and their potentiality is proved.

Keywords: linear complementarity, polyhedral complex, monotonicity, potentiality of mapping, homology group.

UDC: 519.865.3

Received: 02.03.2017

DOI: 10.17377/sibjim.2018.21.000

 English version: Journal of Applied and Industrial Mathematics, 2018, 12:1, 167–176

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