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2009•Journal of Shanghai University of Engineering ScienceRequires access

Convergence of Ishikawa Iterative Sequences with Errors for Asymptotically Nonexpansive Mappings

Xiang Xiao

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Abstract

This paper mainly shows that sufficient and necessary conditions of nonempty fixed points and sufficient and necessary conditions of the modified Ishikawa iteration sequences with errors converged to fixed points for asymptotically nonexpansive mappings of a nonempty closed convex subset in an uniformly convex Banach space.The results presented also extended and improved some recent results.

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What this paper is about

This paper mainly shows that sufficient and necessary conditions of nonempty fixed points and sufficient and necessary conditions of the modified Ishikawa iteration sequences with errors converged to fixed points for asymptotically nonexpansive mappings of a nonempty closed convex subset in an uniformly convex Banach space.The results presented also extended and improved some recent results.

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Available abstract

This paper mainly shows that sufficient and necessary conditions of nonempty fixed points and sufficient and necessary conditions of the modified Ishikawa iteration sequences with errors converged to fixed points for asymptotically nonexpansive mappings of a nonempty closed convex subset in an uniformly convex Banach space.The results presented also extended and improved some recent results.

Key concepts: Banach space, Regular polygon, Fixed point, Convergence (economics), Mathematics, Applied mathematics, Sequence (biology), Iterative method

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