A strongly convergent algorithm for the split common fixed point problem

Research output: Contribution to journalArticle

19 Citations (Scopus)

Abstract

Abstract Recently, Cui and Wang (2014) constructed an algorithm for demicontractive operators that converges weakly, under mild assumptions, to some solution of the split common fixed point problem. In this paper, based on Halpern's type method (1967), we construct an algorithm for demicontractive operators that produces sequences that always converge strongly to a specific solution of the split common fixed point problem. Particular cases of directed operators and quasi-nonexpansive mappings are also considered.

Original languageEnglish
Article number21251
Pages (from-to)844-853
Number of pages10
JournalApplied Mathematics and Computation
Volume265
DOIs
Publication statusPublished - Jun 22 2015

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Fixed Point Problem
Common Fixed Point
Mathematical operators
Operator
Converge
Nonexpansive Mapping

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics

Cite this

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A strongly convergent algorithm for the split common fixed point problem. / Boikanyo, Oganeditse A.

In: Applied Mathematics and Computation, Vol. 265, 21251, 22.06.2015, p. 844-853.

Research output: Contribution to journalArticle

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N2 - Abstract Recently, Cui and Wang (2014) constructed an algorithm for demicontractive operators that converges weakly, under mild assumptions, to some solution of the split common fixed point problem. In this paper, based on Halpern's type method (1967), we construct an algorithm for demicontractive operators that produces sequences that always converge strongly to a specific solution of the split common fixed point problem. Particular cases of directed operators and quasi-nonexpansive mappings are also considered.

AB - Abstract Recently, Cui and Wang (2014) constructed an algorithm for demicontractive operators that converges weakly, under mild assumptions, to some solution of the split common fixed point problem. In this paper, based on Halpern's type method (1967), we construct an algorithm for demicontractive operators that produces sequences that always converge strongly to a specific solution of the split common fixed point problem. Particular cases of directed operators and quasi-nonexpansive mappings are also considered.

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