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Convergence Rate of Some Two-Step Iterative Schemes in Banach Spaces

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  • O. T. Wahab
  • R. O. Olawuyi
  • K. Rauf
  • I. F. Usamot

Abstract

This article proves some theorems to approximate fixed point of Zamfirescu operators on normed spaces for some two-step iterative schemes, namely, Picard-Mann iteration, Ishikawa iteration, S-iteration, and Thianwan iteration, with their errors. We compare the aforementioned iterations using numerical approach; the results show that S-iteration converges faster than other iterations followed by Picard-Mann iteration, while Ishikawa iteration is the least in terms of convergence rate. These results also suggest the best among two-step iterative fixed point schemes in the literature.

Suggested Citation

  • O. T. Wahab & R. O. Olawuyi & K. Rauf & I. F. Usamot, 2016. "Convergence Rate of Some Two-Step Iterative Schemes in Banach Spaces," Journal of Mathematics, Hindawi, vol. 2016, pages 1-8, October.
    • Handle: RePEc:hin:jjmath:9641706
    DOI: 10.1155/2016/9641706
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    1. O. T. Wahab & K. Rauf, 2016. "On Faster Implicit Hybrid Kirk-Multistep Schemes for Contractive-Type Operators," International Journal of Analysis, Hindawi, vol. 2016, pages 1-10, September.
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