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Modified Forward-Backward Splitting Method Without Cocoercivity for the sum of two Monotone Operators in Banach Spaces

dc.contributor.authorAlka, Maryam
dc.date.accessioned2022-08-30T10:19:42Z
dc.date.available2022-08-30T10:19:42Z
dc.date.issued2021-07-10
dc.identifier.urihttp://repository.aust.edu.ng/xmlui/handle/123456789/5075
dc.description2021 Pure and Applied Mathematics Masters Thesesen_US
dc.description.abstractIn this thesis, we present an algorithm for solving a variation inclusion problem of sum of two monotone operators in real Banach spaces which uses variable step sizes that are updated over each iteration by some cheap computations. These step sizes are found without using Linesearch Procedure or prior knowledge of the Lipschitz constant. More precisely, we provide the following theorem. Theorem. Let E be a real 2-uniformly convex and uniformly smooth Banach space. Let A : E → 2E∗ be a maximal monotone operator and B : E → E∗ be monotone and Lipschitz, and assume that (A + B)−1 (0) 6= ∅ and J is weakly sequentially continuous. For x0, x−1 ∈ E define the sequence xn iteratively by xn+1 = J Aλn◦ J−1 (Jxn − λnBxn − λn−1(Bxn − Bxn−1)), n ≥ 0;λn+1 := min λn, θkxn+1 − xnk kBxn+1 − Bxnk , θ ∈ (0,12µ), µ ≥ 1. Then, the sequence {xn} converges weakly to s an element of (A + B)−1(0). Finally, we give some real life physical applications to show how results can be ap plieden_US
dc.description.sponsorshipAUSTen_US
dc.language.isoenen_US
dc.publisherAUSTen_US
dc.subject2021 Pure and Applied Mathematics Masters Thesesen_US
dc.subjectAlka Maryamen_US
dc.subjectDr. A.U. Belloen_US
dc.titleModified Forward-Backward Splitting Method Without Cocoercivity for the sum of two Monotone Operators in Banach Spacesen_US
dc.typeThesisen_US


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