2012•Abstract and Applied AnalysisOpen access

On the Convergence of Mann and Ishikawa Iterative Processes for Asymptotically ϕ‐Strongly Pseudocontractive Mappings

Xuewu Wang, Giuseppe Marino, Luigi Muglia

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Abstract

We prove the equivalence and the strong convergence of (1) the modified Mann iterative process and (2) the modified Ishikawa iterative process for asymptotically ϕ‐strongly pseudocontractive mappings in a uniformly smooth Banach space.

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We prove the equivalence and the strong convergence of (1) the modified Mann iterative process and (2) the modified Ishikawa iterative process for asymptotically ϕ‐strongly pseudocontractive mappings in a uniformly smooth Banach space.

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Available abstract

We prove the equivalence and the strong convergence of (1) the modified Mann iterative process and (2) the modified Ishikawa iterative process for asymptotically ϕ‐strongly pseudocontractive mappings in a uniformly smooth Banach space.

Key concepts: Banach space, Equivalence (formal languages), Mathematics, Convergence (economics), Iterative and incremental development, Applied mathematics, Pure mathematics, Discrete mathematics

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