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Journals / New Trends in Mathematical Sciences / 2017 / Cilt: 5 Sayı: 2

A new two step iterative scheme for a finite family of nonself I-asymptotically nonexpansive mappings in Banach space

Birol Gunduz
Pages
16–28
Publication Date
2017-03-30
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

It presents some new results in this paper.

📌 3 Key Takeaways

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Objective & Hypothesis:Let E be a real uniformly convex Banach space, K be a nonempty closed convex subset of E and let Ti : K → E be N Ii-asymptotically nonexpansive nonself mappings and Ii be N asymptotically nonexpansive nonself mappings.
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Key Findings & Data:It is proved that a new two step iterative algorithm converges weakly to a q ∈ F in a real uniformly convex Banach space such that its dual has the Kadec-Klee property and strongly under condition (B) in a real uniformly convex Banach space.
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Conclusion & Impact:It presents some new results in this paper.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Nonself I-asymptotically nonexpansive mapping · Fr´echet differentiable norm · Opial property

Abstract

Let E be a real uniformly convex Banach space, K be a nonempty closed convex subset of E and let Ti : K → E be N Ii-asymptotically nonexpansive nonself mappings and Ii be N asymptotically nonexpansive nonself mappings. It is proved that a new two step iterative algorithm converges weakly to a q ∈ F in a real uniformly convex Banach space such that its dual has the Kadec-Klee property and strongly under condition (B) in a real uniformly convex Banach space. It presents some new results in this paper.

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Cite This Article

Gunduz, B. (2017). A new two step iterative scheme for a finite family of nonself I-asymptotically nonexpansive mappings in Banach space. New Trends in Mathematical Sciences, Cilt: 5 Sayı: 2, 16–28. https://ajindex.com/articles/1003726

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