Equational Systems on Posets and Their Applications

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In this paper, we introduce the notion of nonlinear equational systems. We consider some important results of equational systems on posets (partially ordered sets) and Banach lattices. Also we see their applications in data-flow analysis—a general theory to solve some special types of simultaneous nonlinear equations on complete lattices—and extend the Cournot oligopoly on Banach lattices. At the end, there are some new theoretical suggestions for decision makers, especially computer program designers, to shorten and optimize their calculations.

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Correspondence to Hamidreza Goudarzi.

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Roointan, G., Goudarzi, H. Equational Systems on Posets and Their Applications. Iran J Sci Technol Trans Sci (2020) doi:10.1007/s40995-019-00808-z

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  • Equational systems
  • Data-flow analysis
  • Partially ordered sets
  • Preserving maps
  • Monotone property
  • Iterative algorithm
  • Banach lattice
  • Cournot oligopoly