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CONVERGENCE OF MANN’S ALTERNATING PROJECTIONS IN CAT($\unicode[STIX]{x1D705}$ ) SPACES

Part of: Equations and inequalities involving nonlinear operators General theory of linear operators Global differential geometry

Published online by Cambridge University Press:  03 May 2018

BYOUNG JIN CHOI Open the ORCID record for BYOUNG JIN CHOI [Opens in a new window]
BYOUNG JIN CHOI*
Affiliation:
Department of Mathematics, Institute for Industrial and Applied Mathematics, Chungbuk National University, Cheongju 28644, Korea email choibj@chungbuk.ac.kr
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Abstract

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We study the convex feasibility problem in $\text{CAT}(\unicode[STIX]{x1D705})$ spaces using Mann’s iterative projection method. To do this, we extend Mann’s projection method in normed spaces to $\text{CAT}(\unicode[STIX]{x1D705})$ spaces with $\unicode[STIX]{x1D705}\geq 0$ , and then we prove the $\unicode[STIX]{x1D6E5}$ -convergence of the method. Furthermore, under certain regularity or compactness conditions on the convex closed sets, we prove the strong convergence of Mann’s alternating projection sequence in $\text{CAT}(\unicode[STIX]{x1D705})$ spaces with $\unicode[STIX]{x1D705}\geq 0$ .

Keywords

convex feasibility problemCAT(𝜅) space𝛥-convergenceMann’s alternating projection method

MSC classification

Primary: 47J25: Iterative procedures
Secondary: 47A46: Chains (nests) of projections or of invariant subspaces, integrals along chains, etc. 53C23: Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 98 , Issue 1 , August 2018 , pp. 134 - 143
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

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