On the strong convergence of a general type Krasnoselskii-Mann’s algorithm depending on the coefficients

Let H be a Hilbert space, (Wn)n∈ℕ a suitable family of mappings, S a nonexpansive mapping and D a strongly monotone operator. We are interested in the strong convergence of the general schemexn+1=γxn+(1−γ)Wn(αnSxn+(1−αn)(I−μnD)xn),γ∈[0,1),in dependence of the coefficients (αn)n∈ℕ and (μn)n∈ℕ .