New iteration process for a general class of contractive mappings

Let K be a closed convex subset of X, and let T : K → K be a self-mapping with the set FT of fixed points such that ‖Tx − ρ‖ ≤ δ‖x − ρ‖ for all x ∈ K, ρ ∈ FT and some δ ∈ (0, 1). We introduce a new iteration process called Picard-hybrid iteration and show that this iteration process converges to the...

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Veröffentlicht in:Acta et commentationes Universitatis Tartuensis de mathematica 2016, Vol.20 (2), p.117-122
1. Verfasser: Mogbademu, Adesanmi Alao
Format: Artikel
Sprache:eng
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Zusammenfassung:Let K be a closed convex subset of X, and let T : K → K be a self-mapping with the set FT of fixed points such that ‖Tx − ρ‖ ≤ δ‖x − ρ‖ for all x ∈ K, ρ ∈ FT and some δ ∈ (0, 1). We introduce a new iteration process called Picard-hybrid iteration and show that this iteration process converges to the unique fixed point of T. It is also shown that our iteration process converges more rapidly than the Picard–Mann and Picard iteration processes. Our result improves a recent result of S. H. Khan and some other results.
ISSN:1406-2283
2228-4699
DOI:10.12697/ACUTM.2016.20.10