Abstract. In this paper, we first introduce some semigroups of mappings
called quasi-nonexpansive, nonspreading, hybrid, TJ-1, TJ-2, and generalized hybrid semigroup. Then, using the theory of invariant means,
we prove fixed point theorems, weak convergence theorem of Mann’s
type and generalized nonlinear ergodic theorem for such semigroups in
a Hilbert space. Furthermore, we prove a strong convergence theorem
of Halpern’s type for the proposed semigroups in a Hilbert space. The
results presented in this paper mainly extend and improved some wellknown results in the literature.