Figure 1

Behavior of $\mathbf{\parallel }\mathit{T}\mathbf{(}{\mathit{x}}_{\mathit{n}}\mathbf{)}\mathbf{-}{\mathit{x}}_{\mathit{n}}\mathbf{\parallel }$ for the Halpern algorithm and Algorithm  3.1 (proposed). (The Halpern algorithm took 850 iterations to satisfy $\parallel T(x_n)-x_n\parallel <{10}^{-6}$, whereas Algorithm 3.1 took only six.)