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

By Naseer Shahzad, A. Udomene. 2006

54 citations recorded by the source corpus.

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 .

Subfields: Computational Theory and Mathematics, Geometry and Topology, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/7e7f0256c66be9d3ded3918ffe23dbec9d1ec051

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In Computational Theory and Mathematics

1. Abdul Rahim Khan
2. Hafiz Fukhar-ud-din
3. A. Domlo

In Geometry and Topology

1. Abdul Rahim Khan
2. Hafiz Fukhar-ud-din
3. A. Domlo

In Numerical Analysis

1. Abdul Rahim Khan
2. Hafiz Fukhar-ud-din
3. A. Domlo

Citations in the corpus

• Common fixed points Noor iteration for a finite family of asymptotically quasi-nonexpansive mappings in Banach spaces (2008, background): “Our work is a significant generalization of the corresponding results of Khan and Takahashi [10], Qihou [20], Schu [23], Shahzad and Udomene [24], Tan and Xu [28] and Xu and Noor [29].”