Bulletin of the Belgian Mathematical Society - Simon Stevin

On Modified Noor Iterations for Asymptotically Nonexpansive Mappings

Abdul Rahim Khan

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The main aim of this paper is to introduce a modified Noor iterations scheme to provide a unified approach to the Mann and Ishikawa iteration processes. We study weak and strong convergence of the new iterations scheme of a nonself asymptotically nonexpansive map satisfying a new control condition in uniformly convex Banach spaces. Several recent results about Mann-type and Ishikawa-type iteration schemes for nonself(self) asymptotically nonexpansive maps follow directly and concurrently from our results.

Article information

Bull. Belg. Math. Soc. Simon Stevin, Volume 17, Number 1 (2010), 127-140.

First available in Project Euclid: 5 March 2010

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47H09: Contraction-type mappings, nonexpansive mappings, A-proper mappings, etc. 47H10: Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30] 65J15: Equations with nonlinear operators (do not use 65Hxx)

Nonself asymptotically nonexpansive map Retract Fixed point Weak and strong convergence Condition (A)


Khan, Abdul Rahim. On Modified Noor Iterations for Asymptotically Nonexpansive Mappings. Bull. Belg. Math. Soc. Simon Stevin 17 (2010), no. 1, 127--140. https://projecteuclid.org/euclid.bbms/1267798503

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