On shrinking projection method for cutter type mappings with nonsummable errors

Autor:	Takanori Ibaraki, Satit Saejung
Jazyk:	angličtina
Rok vydání:	2023
Předmět:	Fixed point Shrinking projection method Cutter type mapping Metric projection Generalized projection Maximal monotone operator Mathematics QA1-939
Zdroj:	Journal of Inequalities and Applications, Vol 2023, Iss 1, Pp 1-20 (2023)
Druh dokumentu:	article
ISSN:	1029-242X
DOI:	10.1186/s13660-023-03004-1
Popis:	Abstract We prove two key inequalities for metric and generalized projections in a certain Banach space. We then obtain some asymptotic behavior of a sequence generated by the shrinking projection method introduced by Takahashi et al. (J. Math. Anal. Appl. 341:276–286, 2008) where the computation allows some nonsummable errors. We follow the idea proposed by Kimura (Banach and Function Spaces IV (ISBFS 2012), pp. 303–311, 2014). The mappings studied in this paper are more general than the ones in (Ibaraki and Kimura in Linear Nonlinear Anal. 2:301–310, 2016; Ibaraki and Kajiba in Josai Math. Monogr. 11:105–120, 2018). In particular, the results in (Ibaraki and Kimura in Linear Nonlinear Anal. 2:301–310, 2016; Ibaraki and Kajiba in Josai Math. Monogr. 11:105–120, 2018) are both extended and supplemented. Finally, we discuss our results for finding a zero of maximal monotone operator and a minimizer of convex functions on a Banach space.
Databáze:	Directory of Open Access Journals
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