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The Equivalence of Mann and Implicit Mann Iterations for Uniformly Pseudocontractive Mappings in Uniformly Smooth Banach Spaces

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Abstract:

In this paper, suppose is an arbitrary uniformly smooth real Banach space, and is a nonempty closed convex subset of . Let be a generalized Lipschitzian and uniformly pseudocontractive self-map with . Suppose that , are defined by Mann iteration and implicit Mann iteration respectively, with the iterative parameter satisfying certain conditions. Then the above two iterations that converge strongly to fixed point of are equivalent.

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Periodical:

Applied Mechanics and Materials (Volumes 50-51)

Pages:

718-722

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.50-51.718

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Cite this paper

Online since:

February 2011

Authors:

Cheng Wang, Zhi Ming Wang

Keywords:

Generalized Lipschitzian Map, Implicit Mann Iteration, Mann Iteration, Uniformly Pseudocontractive Map, Uniformly Smooth Banach Space

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© 2011 Trans Tech Publications Ltd. All Rights Reserved

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References

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