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Fixed Point of a New Three‐Step Iteration Algorithm under Contractive‐Like Operators over Normed Spaces

Author

Listed:
  • Vatan Karakaya
  • Kadri Doğan
  • Faik Gürsoy
  • Müzeyyen Ertürk

Abstract

We introduce a new three‐step iteration scheme and prove that this new iteration scheme is convergent to fixed points of contractive‐like operators. Also, by providing an example, we show that our new iteration method is faster than another iteration method due to Suantai (2005). Furthermore, it is shown that this new iteration method is equivalent to some other iteration methods in the sense of convergence. Finally, it is proved that this new iteration method is T‐stable.

Suggested Citation

  • Vatan Karakaya & Kadri Doğan & Faik Gürsoy & Müzeyyen Ertürk, 2013. "Fixed Point of a New Three‐Step Iteration Algorithm under Contractive‐Like Operators over Normed Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:560258
    DOI: 10.1155/2013/560258
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    References listed on IDEAS

    as
    1. B. E. Rhoades & Ştefan M. Şoltuz, 2006. "The equivalence between the Mann and Ishikawa iterations dealing with generalized contractions," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2006, pages 1-5, July.
    2. B. E. Rhoades & Stefan M. Soltuz, 2003. "On the equivalence of Mann and Ishikawa iteration methods," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2003, pages 1-9, January.
    3. B. E. Rhoades & Ştefan M. Şoltuz, 2003. "The equivalence of Mann iteration and Ishikawa iteration for non-Lipschitzian operators," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2003, pages 1-7, January.
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    Cited by:

    1. Krzysztof Gdawiec & Wiesław Kotarski & Agnieszka Lisowska, 2015. "Polynomiography Based on the Nonstandard Newton‐Like Root Finding Methods," Abstract and Applied Analysis, John Wiley & Sons, vol. 2015(1).

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