Mann and Ishikawa iterative processes for multivalued mappings in Banach spaces

  • Authors:
  • Bancha Panyanak

  • Affiliations:
  • Department of Mathematics, Faculty of Science, Chaing Mai University, Chiang Mai 50200, Thailand

  • Venue:
  • Computers & Mathematics with Applications
  • Year:
  • 2007

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Abstract

Let K be a nonempty compact convex subset of a uniformly convex Banach space, and T:K-P(K) a multivalued nonexpansive mapping. We prove that the sequences of Mann and Ishikawa iterates converge to a fixed point of T. This generalizes former results proved by Sastry and Babu [K.P.R. Sastry, G.V.R. Babu, Convergence of Ishikawa iterates for a multi-valued mapping with a fixed point, Czechoslovak Math. J. 55 (2005) 817-826]. We also introduce both of the iterative processes in a new sense, and prove a convergence theorem of Mann iterates for a mapping defined on a noncompact domain.