Strong convergence theorems with three-step iteration in star-shaped   metric spaces

Byung-Soo  Lee

doi:10.3934/naco.2011.1.371

Article Contents

2011, Volume 1, Issue 3: 371-379. Doi: 10.3934/naco.2011.1.371

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Strong convergence theorems with three-step iteration in star-shaped metric spaces

Byung-Soo Lee^1,

1.
Department of Mathematics, Kyungsung University, Busan 608-736

Received: March 31, 2011

Revised: May 31, 2011

Published: August 2011

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Abstract

The author considers a Noor-type three-step iterative scheme including Ishikawa-type scheme as a special case to approximate common fixed points of an infinite family of uniformly quasi-Lipschitzian mappings and an infinite family of nonexpansive mappings in star-shaped metric spaces. His results are cases of star-shaped metric space of results shown in [7].

Keywords:

Star-shaped metric space,
Noor-type iteration,
$f$-expansive mapping,
uniformly quasi-$\sup(f)$-Lipschitzian mapping.

Mathematics Subject Classification: 47H10, 47H17, 49J40.

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References

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