TY - JOUR

T1 - Polyhedral Complementarity on a Simplex. Potentiality of Regular Mappings

AU - Shmyrev, V. I.

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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.

AB - 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.

KW - homology group

KW - linear complementarity

KW - monotonicity

KW - polyhedral complex

KW - potentiality of mapping

UR - http://www.scopus.com/inward/record.url?scp=85043239409&partnerID=8YFLogxK

U2 - 10.1134/S1990478918010155

DO - 10.1134/S1990478918010155

M3 - Article

AN - SCOPUS:85043239409

VL - 12

SP - 167

EP - 176

JO - Journal of Applied and Industrial Mathematics

JF - Journal of Applied and Industrial Mathematics

SN - 1990-4789

IS - 1

ER -