2022
DOI: 10.3934/math.2022412
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One step proximal point schemes for monotone vector field inclusion problems

Abstract: <abstract><p>In this paper, we propose one step convex combination of proximal point algorithms for countable collection of monotone vector fields in CAT(0) spaces. We establish $ \Delta $-convergence and strong convergence theorems for approximating a common solution of a countable family of monotone vector field inclusion problems. Furthermore, we apply our methods to solve a family of minimization problems, compute Frechét mean and geometric median in CAT(0) spaces, and solve a kinematic problem… Show more

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Cited by 6 publications
(4 citation statements)
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“…, converge strongly to a solution of (34). for all u, w ∈  and the solution set of ( 34) is nonempty.…”
Section: This and The Hypothesis Thatmentioning
confidence: 99%
See 1 more Smart Citation
“…, converge strongly to a solution of (34). for all u, w ∈  and the solution set of ( 34) is nonempty.…”
Section: This and The Hypothesis Thatmentioning
confidence: 99%
“…Moreover, our convergence result is established for mappings satisfying (3), which represents a less restrictive condition than the existing convergence results in the same setting. Our framework allows us to transform non-monotone (and non-convex) problems into monotone (convex) problems within the context of geodesic spaces [33][34][35]. To the best of our knowledge, this marks the first instance where problem (2) is considered within the framework of Hadamard spaces with the class of mappings satisfying the monotone type condition (3).…”
Section: Introductionmentioning
confidence: 99%
“…set) can be viewed as convex function (rep. set) [19]. Some brilliant known results in CAT(0)$$ \mathrm{CAT}(0) $$ spaces can be found in previous studies [20–27] and references therein.…”
Section: Cat(0) Spacesmentioning
confidence: 99%
“…The theory of V.I.P. combines concepts of nonlinear operators and convex analysis in such a way that it generalizes both and is used to model nonlinear problems of physical phenomena in economics, sciences and engineering [3][4][5][6].…”
Section: Introductionmentioning
confidence: 99%