A new technique for convergence theorem of fixed point problem of quasi-nonexpansive mapping

© 2015, Cheawchan et al. For the purpose of this paper, we use the method different from the relaxed extragradient method for finding a common element of the set of fixed points of a quasi-nonexpansive mapping, the set of solutions of equilibrium problems, and the set of solutions of a modified syst...

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Bibliographic Details
Main Authors: Kanyarat Cheawchan, Suthep Suantai, Atid Kangtunyakarn
Format: Journal
Published: 2018
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Online Access:https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=84948417278&origin=inward
http://cmuir.cmu.ac.th/jspui/handle/6653943832/54638
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Institution: Chiang Mai University
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Summary:© 2015, Cheawchan et al. For the purpose of this paper, we use the method different from the relaxed extragradient method for finding a common element of the set of fixed points of a quasi-nonexpansive mapping, the set of solutions of equilibrium problems, and the set of solutions of a modified system of variational inequalities without demiclosed condition of W and Wω:=(1−ω)I+ωW, where W is a quasi-nonexpansive mapping and (Formula presented.) in the framework of Hilbert space. By using our main result, we obtain a strong convergence theorem involving a finite family of nonspreading mappings and another corollary. Moreover, we give a numerical example to encourage our main theorem.