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

Published online by Cambridge University Press:  03 May 2018

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 $\unicode[STIX]{x1D705}\geq 0$.

Type
Research Article
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

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