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2021•Results in Nonlinear AnalysisOpen access

The Convergence of Ishikawa Iteration for Generalized Φ-contractive Mappings

Linxin Lİ, Dingping Wu

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Abstract

Charles[1] proved the convergence of Picard-type iterative for generalized Φ− accretive non-self maps in a real uniformly smooth Banach space. Based on the theorems of the zeros of strongly Φ− quasi- accretive and fixed points of strongly Φ− hemi-contractions, we extend the results to Ishikawa iterative and Ishikawa iteration process with er- rors for generalized Φ− hemi-contractive maps .

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Charles[1] proved the convergence of Picard-type iterative for generalized Φ− accretive non-self maps in a real uniformly smooth Banach space. Based on the theorems of the zeros of strongly Φ− quasi- accretive and fixed points of strongly Φ− hemi-contractions, we extend the results to Ishikawa iterative and Ishikawa iteration process with er- rors for generalized Φ− hemi-contractive maps .

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Available abstract

Charles[1] proved the convergence of Picard-type iterative for generalized Φ− accretive non-self maps in a real uniformly smooth Banach space. Based on the theorems of the zeros of strongly Φ− quasi- accretive and fixed points of strongly Φ− hemi-contractions, we extend the results to Ishikawa iterative and Ishikawa iteration process with er- rors for generalized Φ− hemi-contractive maps .

Key concepts: Convergence (economics), Mathematics, Banach space, Fixed point, Fixed-point iteration, Applied mathematics, Iterative and incremental development, Type (biology)

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