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Strong convergence theorems of an iterative scheme for strictly pseudocontractive mappings in Banach spaces

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Abstract The article establishes the sufficient and necessary conditions for the strong convergence of the Ishikawa iterative scheme with random errors in the sense of Xu for a strictly pseudocontractive… Click to show full abstract

Abstract The article establishes the sufficient and necessary conditions for the strong convergence of the Ishikawa iterative scheme with random errors in the sense of Xu for a strictly pseudocontractive mapping in an arbitrary real Banach space under certain assumptions. It affirmatively answers the open question that put forth by Zeng. The results in this paper extend and improve the corresponding results of Browder, Petryshyn, Rhoades, Osilike and Zeng.

Keywords: iterative scheme; banach; strong convergence; strictly pseudocontractive

Journal Title: Optimization
Year Published: 2018

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