Strong convergence theorems of <Emphasis Type="Italic">k</Emphasis>-strict pseudo-contractions in Hilbert spaces

Let K be a nonempty closed convex subset of a real Hilbert space H such that K ± K ⊂ K, T: K → H a k-strict pseudo-contraction for some 0 ⩽ k < 1 such that F(T) = {x ∈ K: x = Tx} ≠ $ \not 0 $ \not 0 . Consider the following iterative algorithm given by

$ \forall x_1 \in K,x_{n + 1} = \alpha _n \gamma f(x_n ) + \beta _n x_n + ((1 - \beta _n )I - \alpha _n A)P_K Sx_{n,} n \geqslant 1, $ \forall x_1 \in K,x_{n + 1} = \alpha _n \gamma f(x_n ) + \beta _n x_n + ((1 - \beta _n )I - \alpha _n A)P_K Sx_{n,} n \geqslant 1,
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