Table 2 Iterates of S-iteration, Mann iteration, and Ishikawa iteration for \(x_{1} =u_{1}=z_{1}= 0.4\)
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 | 0.4000000 | – | 0.4000000 | – | 0.4000000 | – |
2 | 0.7181818 | 3.1818e − 01 | 0.5000000 | 1.0000e − 01 | 0.5181818 | 1.1818e − 01 |
3 | 0.8669850 | 1.4880e − 01 | 0.6176471 | 1.1765e − 01 | 0.6450471 | 1.2687e − 01 |
4 | 0.9370031 | 7.0018e − 02 | 0.7219251 | 1.0428e − 01 | 0.7512207 | 1.0617e − 01 |
5 | 0.9700950 | 3.3092e − 02 | 0.8043177 | 8.2393e − 02 | 0.8312256 | 8.0005e − 02 |
⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ | ⋮ |
16 | 0.9999913 | 9.5358e − 06 | 0.9981890 | 1.0448e − 03 | 0.9989430 | 6.6918e − 04 |
17 | 0.9999958 | 4.5591e − 06 | 0.9988551 | 6.6612e − 04 | 0.9993547 | 4.1173e − 04 |
18 | 0.9999980 | 2.1802e − 06 | 0.9992782 | 4.2311e − 04 | 0.9996071 | 2.5242e − 04 |
19 | 0.9999990 | 1.0428e − 06 | 0.9995461 | 2.6788e − 04 | 0.9997614 | 1.5427e − 04 |
20 | 0.9999995 | 4.9889e − 07 | 0.9997152 | 1.6910e − 04 | 0.9998554 | 9.4011e − 05 |