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Approximating common fixed points of two asymptotically quasi-nonexpansive mappings in Banach spaces

Fixed Point Theory and Applications volume 2006, Article number: 18909 (2006) Cite this article

Abstract

Suppose is a nonempty closed convex subset of a real Banach space . Let be two asymptotically quasi-nonexpansive maps with sequences such that and , and . Suppose is generated iteratively by where and are real sequences in . It is proved that (a) converges strongly to some if and only if ; (b) if is uniformly convex and if either or is compact, then converges strongly to some . Furthermore, if is uniformly convex, either or is compact and is generated by , where , are bounded, are real sequences in such that and , are summable; it is established that the sequence (with error member terms) converges strongly to some .

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Authors and Affiliations

  1. Department of Mathematics, King Abdul Aziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia

    Naseer Shahzad

  2. Department of Mathematics/Statistics/Computer Science, University of Port Harcourt, PMB, Port Harcourt, 5323, Nigeria

    Aniefiok Udomene

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  1. Naseer Shahzad
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  2. Aniefiok Udomene
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Correspondence to Naseer Shahzad.

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Shahzad, N., Udomene, A. Approximating common fixed points of two asymptotically quasi-nonexpansive mappings in Banach spaces. Fixed Point Theory Appl 2006, 18909 (2006). https://doi.org/10.1155/FPTA/2006/18909

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  • DOI: https://doi.org/10.1155/FPTA/2006/18909

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