*-μ-semirings and *-λ-semirings

We introduce and study *-μ-semirings and *-λ-semirings which generalize inductive *-semirings and weak inductive *-semirings, respectively. Also, we discuss the semiring of formal power series with coefficients in such a semiring and prove that the semiring of formal power series with coefficients in a weak inductive *-semiring [μ-semiring, λ-semiring, *-λ-semiring] is a weak inductive *-semirng [μ-semiring, λ-semiring, *-λ-semiring, respectively]. This gives a positive answer to one of Ésik and Kuich's open problems.