$\unicode[STIX]{x1D6E5}$-CONVERGENCES OF WEIGHTED AVERAGED PROJECTIONS IN $\text{CAT}(\unicode[STIX]{x1D705})$ SPACES. (14th June 2021)

• Record Type: Journal Article
• Authors: CHOI, BYOUNG JIN
• Is Part Of: Journal of the Australian Mathematical Society. Volume 110:Number 3(2021)
• Page Start: 289
• Page End: 301
• Publication Date: 2021-06-14
• Subjects: 47J25, -- 47A46, -- 53C23; convex feasibility problem, -- CAT(𝜅) space, -- weighted averaged projection method, -- averaged projection method, -- 𝛥-convergence; Mathematics -- Periodicals; Statistics -- Periodicals; Mathematical statistics -- Periodicals; 510.5
• DOI: 10.1017/S1446788720000191
• Languages: English
• ISSNs: 1446-7887

Abstract

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.