Strong convergence of the Ishikawa iteration for Lipschitz α-hemicontractive mappings
نویسندگان
چکیده
منابع مشابه
Strong convergence of the Mann iteration for α-demicontractive mappings
The paper deals with strong convergence properties of the Mann iteration. A new class of demicontractive mappings (called α-demicontractive) is introduced for which the strong convergence of the computed sequence is assured. The paper presents also an overview of relevant contributions of the last two decades, concerning strong convergence for Mann-type iteration of demicontractive mappings.
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Let q > 1 and E be a real q-uniformly smooth Banach space, K be a nonempty closed convex subset of E and T : K → K be a Lipschitz continuous mapping. Let {un} and {vn} be bounded sequences in K and {αn} and {βn} be real sequences in [0, 1] satisfying some restrictions. Let {xn} be the sequence generated from an arbitrary x1 ∈ K by the Ishikawa iteration process with errors: yn = (1− βn)xn + βnT...
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and Applied Analysis 3 In 2005, C. E. Chidume and C. O. Chidume 3 proved the convergence theorems for fixed points of uniformly continuous generalized Φ-hemicontractive mappings and published in 3 . However, there exists a gap in the proof course of their theorems. The aim of this paper is to show the convergence of the multistep iteration with errors for fixed points of uniformly continuous Φ-...
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ژورنال
عنوان ژورنال: Annals of West University of Timisoara - Mathematics and Computer Science
سال: 2015
ISSN: 1841-3307
DOI: 10.1515/awutm-2015-0008