PROCEEDINGS IPMU '08

Contraction and Dilation Operators in a Semilinear Space over Residuated Lattice

Irina Perfilieva.

The notion of a semilinear space
over residuated lattice is introduced.
Two problems of solvability of systems
of linear-like equations with
sup -* or inf → compositions are
considered in a finite semilinear
space. We prove that each system
of equations is solvable if and only
if its right-hand side is a fixed point
of the respective contraction or dilation
operator. Sets of fixed points
are characterized as subsemimodules
over respective reducts of the residuated
l-monoid.

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