On best proximity results for a generalized modified Ishikawa’s iterative scheme driven by perturbed 2-cyclic like-contractive self-maps in uniformly convex Banach spaces

dc.contributor.authorDe la Sen, M.
dc.contributor.authorAbbas, Mujahid
dc.date.accessioned2020-03-18T11:53:44Z
dc.date.available2020-03-18T11:53:44Z
dc.date.issued2019-01-30
dc.description.abstractThis paper proposes a generalized modified iterative scheme where the composed self-mapping driving can have distinct step-dependent composition order in both the auxiliary iterative equation and the main one integrated in Ishikawa’s scheme. The self-mapping which drives the iterative scheme is a perturbed -cyclic one on the union of two sequences of nonempty closed subsets and of a uniformly convex Banach space. As a consequence of the perturbation, such a driving self-mapping can lose its cyclic contractive nature along the transients of the iterative process. These sequences can be, in general, distinct of the initial subsets due to either computational or unmodeled perturbations associated with the self-mapping calculations through the iterative process. It is assumed that the set-theoretic limits below of the sequences of sets and exist. The existence of fixed best proximity points in the set-theoretic limits of the sequences to which the iterated sequences converge is investigated in the case that the cyclic disposal exists under the asymptotic removal of the perturbations or under its convergence of the driving self-mapping to a limit contractive cyclic structure.en_ZA
dc.description.departmentMathematics and Applied Mathematicsen_ZA
dc.description.librarianam2020en_ZA
dc.description.sponsorshipThe Spanish Government and the European Fund of Regional Development FEDER through Grant DPI2015-64766-R as well as UPV /EHU through Grant PGC 17/33.en_ZA
dc.description.urihttps://www.hindawi.com/journals/jmathen_ZA
dc.identifier.citationDe La Sen, M. & Abbas, M. 2019, 'On best proximity results for a generalized modified Ishikawa’s iterative scheme driven by perturbed 2-cyclic like-contractive self-maps in uniformly convex Banach spaces', Journal of Mathematics, vol. 2019, art. 1356918, pp. 1-15.en_ZA
dc.identifier.issn2314-4629 (print)
dc.identifier.issn2314-4785 (online)
dc.identifier.issn10.1155/2019/1356918
dc.identifier.urihttp://hdl.handle.net/2263/73803
dc.language.isoenen_ZA
dc.publisherHindawien_ZA
dc.rights© 2019 M. De la Sen and Mujahid Abbas. This is an open access article distributed under the Creative Commons Attribution License.en_ZA
dc.subjectIterative schemeen_ZA
dc.subjectIshikawa’s schemeen_ZA
dc.subjectSelf-mappingen_ZA
dc.subjectBanach spaceen_ZA
dc.titleOn best proximity results for a generalized modified Ishikawa’s iterative scheme driven by perturbed 2-cyclic like-contractive self-maps in uniformly convex Banach spacesen_ZA
dc.typeArticleen_ZA

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