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

Pages: 371 - 379, Volume 1, Issue 3, September 2011

doi:10.3934/naco.2011.1.371       Abstract        References        Full Text (162.5K)       Related Articles

Byung-Soo Lee - Department of Mathematics, Kyungsung University, Busan 608-736, South Korea (email)

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.

Received: April 2011;      Revised: June 2011;      Published: September 2011.

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