Abstract
Let S = (S, +, ·, *, 0, 1, ≤) be a weak inductive *-semiring. The collection of all n × n matrices S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n×n</sup> , equipped with the usual matrix operations +, · and the unary operation * defined in [3], form a *-semiring. Esik and Kuich propose a open problem that whether the semiring S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n×n</sup> is weak inductive. In this paper, we investigate the case n = 2. It is shows that if S is both a commutative semiring and a λ-semiring, then S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2×2</sup> is weak inductive. By using this result we determine the least simultaneous fixed point of a system of equation proposed in [5], if it is do exist.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
