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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

  AK Vatan Two-step Thakur New Picard-S
\(x_{0}\) 0.9 0.9 0.9 0.9
\(x_{1}\) \(8.6133\times 10^{-2}\) \(1.7227\times 10^{-1}\) \(2.1797\times 10^{-1}\) \(2.1797\times 10^{-1}\)
\(x_{2}\) \(8.2432\times 10^{-3}\) \(3.2973\times 10^{-2}\) \(5.2789\times 10^{-2}\) \(5.2789\times 10^{-2}\)
\(x_{3}\) \(7.889\times 10^{-4}\) \(6.3112\times 10^{-3}\) \(1.2785\times 10^{-2}\) \(1.2785\times 10^{-2}\)
\(x_{4}\) \(7.55\times 10^{-5}\) \(1.208\times 10^{-3}\) \(3.0963\times 10^{-3}\) \(3.0963\times 10^{-3}\)
\(x_{5}\) \(7.2256\times 10^{-6}\) \(2.3122\times 10^{-4}\) \(7.499\times 10^{-4}\) \(7.499\times 10^{-4}\)
\(x_{6}\) \(6.9151\times 10^{-7}\) \(4.4257\times 10^{-5}\) \(1.8162\times 10^{-4}\) \(1.8162\times 10^{-4}\)
\(x_{7}\) \(6.618\times 10^{-8}\) \(8.471\times 10^{-6}\) \(4.3985\times 10^{-5}\) \(4.3985\times 10^{-5}\)
\(x_{8}\) \(6.3336\times 10^{-9}\) \(1.6214\times 10^{-6}\) \(1.0653\times 10^{-5}\) \(1.0653\times 10^{-5}\)
\(x_{9}\) \(6.0615\times 10^{-10}\) \(3.1035\times 10^{-7}\) \(2.5799\times 10^{-6}\) \(2.5799\times 10^{-6}\)
\(x_{10}\) \(5.801\times 10^{-11}\) \(5.9402\times 10^{-8}\) \(6.2483\times 10^{-7}\) \(6.2483\times 10^{-7}\)