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Comparison of fastness of the convergence among Krasnoselskij, Mann, and Ishikawa iterations in arbitrary real Banach spaces

Abstract

Let be an arbitrary real Banach space and a nonempty, closed, convex (not necessarily bounded) subset of . If is a member of the class of Lipschitz, strongly pseudocontractive maps with Lipschitz constant , then it is shown that to each Mann iteration there is a Krasnosleskij iteration which converges faster than the Mann iteration. It is also shown that the Mann iteration converges faster than the Ishikawa iteration to the fixed point of .

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Correspondence to GVR Babu.

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Babu, G., Vara Prasad, K. Comparison of fastness of the convergence among Krasnoselskij, Mann, and Ishikawa iterations in arbitrary real Banach spaces. Fixed Point Theory Appl 2006, 35704 (2007). https://doi.org/10.1155/FPTA/2006/35704

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  • DOI: https://doi.org/10.1155/FPTA/2006/35704

Keywords

  • Banach Space
  • Differential Geometry
  • Computational Biology
  • Real Banach Space
  • Ishikawa Iteration