New iteration process for a general class of contractive mappings

Adesanmi Alao Mogbademu

Abstract


Let K be a closed convex subset of X, and let T : KK be a self-mapping with the set FT of fixed points such that ‖Txρ‖ ≤ δxρ‖ for all xK, ρFT 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.

Keywords


hybrid iteration process; Banach space; fixed point; contractive operators

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DOI: http://dx.doi.org/10.12697/ACUTM.2016.20.10

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ISSN 1406–2283 (print)
ISSN 2228–4699 (online)