Strong convergence for a countable family of strict pseudocontractions in q-uniformly smooth Banach spaces

We introduce a new iterative algorithm for finding a common fixed point of a countable family of strict pseudocontractions in q-uniformly smooth and uniformly convex Banach spaces. We then prove that the sequence generated by the proposed algorithm converges strongly to a common fixed point of an in...

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Bibliographic Details
Main Authors: Prasit Cholamjiak, Suthep Suantai
Format: Journal
Published: 2018
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Online Access:https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=79960181401&origin=inward
http://cmuir.cmu.ac.th/jspui/handle/6653943832/49884
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Institution: Chiang Mai University
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Summary:We introduce a new iterative algorithm for finding a common fixed point of a countable family of strict pseudocontractions in q-uniformly smooth and uniformly convex Banach spaces. We then prove that the sequence generated by the proposed algorithm converges strongly to a common fixed point of an infinite family of strict pseudocontractions. Our results mainly improve and extend the results announced by Yao et al. [Y. Yao, Y.-C. Liou, G. Marino, Strong convergence of two iterative algorithms for nonexpansive mappings in Hilbert spaces, Fixed Point Theory Appl. 2009 (2009) 7 pages. doi:10.1155/2009/279058. Art. ID 279058]. © 2011 Elsevier Ltd. All rights reserved.