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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

  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