Table 1 Iterative values of AK, Vatan Two-step, Thakur New and Picard-S iteration processes for mapping \(T(x)=\frac{x}{2},\) where \(\alpha _{n}=\beta _{n}=\frac{1}{4},\) for all n
From: On different results for new three step iteration process in Banach spaces
| Â | AK | Vatan Two-step | Thakur New | Picard-S |
|---|---|---|---|---|
\(x_{0}\) | 0.9 | 0.9 | 0.9 | 0.9 |
\(x_{1}\) | \(8.6133\times 10^{-2}\) | \(1.7227\times 10^{-1}\) | \(2.1797\times 10^{-1}\) | \(2.1797\times 10^{-1}\) |
\(x_{2}\) | \(8.2432\times 10^{-3}\) | \(3.2973\times 10^{-2}\) | \(5.2789\times 10^{-2}\) | \(5.2789\times 10^{-2}\) |
\(x_{3}\) | \(7.889\times 10^{-4}\) | \(6.3112\times 10^{-3}\) | \(1.2785\times 10^{-2}\) | \(1.2785\times 10^{-2}\) |
\(x_{4}\) | \(7.55\times 10^{-5}\) | \(1.208\times 10^{-3}\) | \(3.0963\times 10^{-3}\) | \(3.0963\times 10^{-3}\) |
\(x_{5}\) | \(7.2256\times 10^{-6}\) | \(2.3122\times 10^{-4}\) | \(7.499\times 10^{-4}\) | \(7.499\times 10^{-4}\) |
\(x_{6}\) | \(6.9151\times 10^{-7}\) | \(4.4257\times 10^{-5}\) | \(1.8162\times 10^{-4}\) | \(1.8162\times 10^{-4}\) |
\(x_{7}\) | \(6.618\times 10^{-8}\) | \(8.471\times 10^{-6}\) | \(4.3985\times 10^{-5}\) | \(4.3985\times 10^{-5}\) |
\(x_{8}\) | \(6.3336\times 10^{-9}\) | \(1.6214\times 10^{-6}\) | \(1.0653\times 10^{-5}\) | \(1.0653\times 10^{-5}\) |
\(x_{9}\) | \(6.0615\times 10^{-10}\) | \(3.1035\times 10^{-7}\) | \(2.5799\times 10^{-6}\) | \(2.5799\times 10^{-6}\) |
\(x_{10}\) | \(5.801\times 10^{-11}\) | \(5.9402\times 10^{-8}\) | \(6.2483\times 10^{-7}\) | \(6.2483\times 10^{-7}\) |