• Title/Summary/Keyword: hybrid multivalued mapping

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WEAK AND STRONG CONVERGENCE THEOREMS FOR THE MODIFIED ISHIKAWA ITERATION FOR TWO HYBRID MULTIVALUED MAPPINGS IN HILBERT SPACES

  • Cholamjiak, Watcharaporn;Chutibutr, Natchaphan;Weerakham, Siwanat
    • Communications of the Korean Mathematical Society
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    • v.33 no.3
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    • pp.767-786
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    • 2018
  • In this paper, we introduce new iterative schemes by using the modified Ishikawa iteration for two hybrid multivalued mappings in a Hilbert space. We then obtain weak convergence theorem under suitable conditions. We use CQ and shrinking projection methods with Ishikawa iteration for obtaining strong convergence theorems. Furthermore, we give examples and numerical results for supporting our main results.

An Ishikawa Iteration Scheme for two Nonlinear Mappings in CAT(0) Spaces

  • Sokhuma, Kritsana
    • Kyungpook Mathematical Journal
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    • v.59 no.4
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    • pp.665-678
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    • 2019
  • We construct an iteration scheme involving a hybrid pair of mappings, one a single-valued asymptotically nonexpansive mapping t and the other a multivalued nonexpansive mapping T, in a complete CAT(0) space. In the process, we remove a restricted condition (called the end-point condition) from results of Akkasriworn and Sokhuma [1] and and use this to prove some convergence theorems. The results concur with analogues for Banach spaces from Uddin et al. [16].