Table 2 Iterative values of AK, Vatan Two-step, Thakur New and Picard-S iteration processes for \(\alpha _{n}=\beta _{n}=\frac{1}{4},\) for all n and mapping \(T(x)=(x+2)^{\frac{1}{3}}\)
From: On different results for new three step iteration process in Banach spaces
| Â | AK | Vatan Two-step | Thakur New | Picard-S |
|---|---|---|---|---|
\(x_{0}\) | 1.99 | 1.99 | 1.99 | 1.99 |
\(x_{1}\) | 1.522210596157901 | 1.527152378405542 | 1.530163443560674 | 1.530160376515624 |
\(x_{2}\) | 1.521381239904628 | 1.521453635507796 | 1.521551978236029 | 1.521551916843118 |
\(x_{3}\) | 1.521379709633547 | 1.521380654057891 | 1.521383088492668 | 1.521383087287047 |
\(x_{4}\) | 1.521379706809788 | 1.521379718941864 | 1.521379773188262 | 1.521379773164595 |
\(x_{5}\) | 1.521379706804577 | 1.521379706960085 | 1.521379708107703 | 1.521379708107238 |
\(x_{6}\) | 1.521379706804568 | 1.521379706806560 | 1.521379706830149 | 1.521379706830139 |
\(x_{7}\) | 1.521379706804568 | 1.521379706804593 | 1.521379706805070 | 1.521379706805069 |
\(x_{8}\) | 1.521379706804568 | 1.521379706804568 | 1.521379706804577 | 1.521379706804577 |
\(x_{9}\) | 1.521379706804568 | 1.521379706804568 | 1.521379706804568 | 1.521379706804568 |
\(x_{10}\) | 1.521379706804568 | 1.521379706804568 | 1.521379706804568 | 1.521379706804568 |
\(x_{11}\) | 1.521379706804568 | 1.521379706804568 | 1.521379706804568 | 1.521379706804568 |