Constructive techniques for zeros of monotone mappings in certain Banach spaces

Let E be a 2-uniformly convex real Banach space with uniformly Gâteaux differentiable norm, and [Formula: see text] its dual space. Let [Formula: see text] be a bounded strongly monotone mapping such that [Formula: see text] For given [Formula: see text] let [Formula: see text] be generated by the a...

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Detalles Bibliográficos
Autores principales: Diop, C, Sow, T M M, Djitte, N, Chidume, C E
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2015
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4516154/
https://www.ncbi.nlm.nih.gov/pubmed/26240781
http://dx.doi.org/10.1186/s40064-015-1169-2
Descripción
Sumario:Let E be a 2-uniformly convex real Banach space with uniformly Gâteaux differentiable norm, and [Formula: see text] its dual space. Let [Formula: see text] be a bounded strongly monotone mapping such that [Formula: see text] For given [Formula: see text] let [Formula: see text] be generated by the algorithm: [Formula: see text] where J is the normalized duality mapping from E into [Formula: see text] and [Formula: see text] is a real sequence in (0, 1) satisfying suitable conditions. Then it is proved that [Formula: see text] converges strongly to the unique point [Formula: see text] Finally, our theorems are applied to the convex minimization problem.

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