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$\unicode[STIX]{x1D6E5}$-CONVERGENCES OF WEIGHTED AVERAGED PROJECTIONS IN $\text{CAT}(\unicode[STIX]{x1D705})$ SPACES

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

Published online by Cambridge University Press:  14 May 2020

BYOUNG JIN CHOI
BYOUNG JIN CHOI*
Affiliation:
Department of Mathematics Education,Jeju National University, Jeju63243, Korea
*
e-mail: choibj@jejunu.ac.kr
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Abstract

We first introduce the weighted averaged projection sequence in $\text{CAT}(\unicode[STIX]{x1D705})$ spaces and then we establish some inequalities for the weighted averaged projection sequence. Using the inequalities, we prove the asymptotic regularity and the $\unicode[STIX]{x1D6E5}$-convergence of the weighted averaged projection sequence. Furthermore, we prove the strong convergence of the sequence under certain regularity or compactness conditions on $\text{CAT}(\unicode[STIX]{x1D705})$ spaces.

Keywords

convex feasibility problemCAT(𝜅) spaceweighted averaged projection methodaveraged projection method𝛥-convergence

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
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 110 , Issue 3 , June 2021 , pp. 289 - 301
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Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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Footnotes

Communicated by G. Wilkin

The author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2017R1C1B1005334) and the 2020 scientific promotion program funded by Jeju National University.

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