A Strong Convergence Theorem for Zeros of Bounded Maximal Monotone Mappings in Banach Spaces with Applications
dc.contributor.author | Uba, Markajoe Olunna | |
dc.date.accessioned | 2017-01-16T13:10:23Z | |
dc.date.available | 2017-01-16T13:10:23Z | |
dc.date.issued | 2016-06-07 | |
dc.identifier.uri | http://repository.aust.edu.ng:8080/xmlui/handle/123456789/570 | |
dc.description.abstract | Let E be a uniformly convex and uniformly smooth real Banach space and E ∗ be its dual. Let A : E → 2 E be a bounded maximal monotone map. Assume that A −1 (0) 6 = ∅. A new iterative sequence is constructed which converges strongly to an element of A −1 (0). The theorem proved, complements results obtained on strong convergence of the proximal point algorithm for approximating an element of A −1 (0) (assuming existence) and also resolves an important open question. Furthermore, this result is applied to convex optimization problems and to variational inequality problems. These results are achieved by combining a theorem of Riech on the strong convergence of the resolvent of maximal monotone mappings in a uniformly smooth real Banach space; new geometric properties of uniformly convex and uniformly smooth real Banach spaces introduced by Alber with a technique of proof which is also of independent interest. | en_US |
dc.language.iso | en | en_US |
dc.subject | Uba Olunna Markajoe | en_US |
dc.subject | Prof Charles Chidume | en_US |
dc.subject | 2016 Pure and Applied Mathematics Theses | en_US |
dc.subject | Convergence Theorem | en_US |
dc.subject | Mappings | en_US |
dc.subject | Banach Spaces | en_US |
dc.title | A Strong Convergence Theorem for Zeros of Bounded Maximal Monotone Mappings in Banach Spaces with Applications | en_US |
dc.type | Thesis | en_US |
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Pure and Applied Mathematics53
This collection contains master's Theses of Pure and Applied Mathematics from 2009 to 2022.