Table 1 Iterates of S-iteration, Mann iteration, and Ishikawa iteration for \(x_{1} =u_{1}=z_{1}= -0.5\)
n | S-iteration | Mann iteration | Ishikawa iteration | |||
|---|---|---|---|---|---|---|
\(x_{n}\) | \(|x_{n}-x_{n-1}|\) | \(u_{n}\) | \(|u_{n}-u_{n-1}|\) | \(z_{n}\) | \(|z_{n}-z_{n-1}|\) | |
1 | −0.5000000 | – | −0.5000000 | – | −0.5000000 | – |
2 | 0.6742424 | 1.1742e + 00 | −0.0833333 | 4.1667e − 01 | −0.1590909 | 3.4091e − 01 |
3 | 0.8462461 | 1.7200e − 01 | 0.2107843 | 2.9412e − 01 | 0.1550166 | 3.1411e − 01 |
4 | 0.9271811 | 8.0935e − 02 | 0.4260250 | 2.1524e − 01 | 0.4077682 | 2.5275e − 01 |
5 | 0.9654324 | 3.8251e − 02 | 0.5960916 | 1.7007e − 01 | 0.5982240 | 1.9046e − 01 |
⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ |
16 | 0.9999899 | 1.1023e − 05 | 0.9962619 | 2.1566e − 03 | 0.9974837 | 1.5930e − 03 |
17 | 0.9999952 | 5.2699e − 06 | 0.9976368 | 1.3749e − 03 | 0.9984638 | 9.8015e − 04 |
18 | 0.9999977 | 2.5201e − 06 | 0.9985102 | 8.7334e − 04 | 0.9990648 | 6.0091e − 04 |
19 | 0.9999989 | 1.2054e − 06 | 0.9990631 | 5.5292e − 04 | 0.9994320 | 3.6724e − 04 |
20 | 0.9999995 | 5.7667e − 07 | 0.9994121 | 3.4904e − 04 | 0.9996558 | 2.2380e − 04 |