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  • Research Article
  • Open Access

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

Fixed Point Theory and Applications20072006:35704

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

  • Received: 25 April 2006
  • Accepted: 4 September 2006
  • Published:

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 .

Keywords

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

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Authors’ Affiliations

(1)
Department of Mathematics, Andhra University, Visakhapatnam, 530 003, India
(2)
Department of Mathematics, Dr. L. Bullayya College, Visakhapatnam, 530 013, India

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