Contraction and Dilation Operators in a Semilinear Space over Residuated Lattice

TL;DRAbstract

The notion of a semilinear space over residuated lattice is introduced. Two problems of solvability of sys-tems 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 di-lation operator. Sets of fixed points are characterized as subsemimodules over respective reducts of the resid-uated l-monoid.

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