期刊论文详细信息
Journal of Inequalities and Applications
On shrinking projection method for cutter type mappings with nonsummable errors
Research
Takanori Ibaraki1  Satit Saejung2 
[1] Department of Mathematics Education, Yokohama National University, Tokiwadai, Hodogaya-ku, 240-8501, Yokohama, Japan;Department of Mathematics, Faculty of Science, Khon Kaen University, 40002, Khon Kaen, Thailand;
关键词: Fixed point;    Shrinking projection method;    Cutter type mapping;    Metric projection;    Generalized projection;    Maximal monotone operator;    47H09;   
DOI  :  10.1186/s13660-023-03004-1
 received in 2022-04-29, accepted in 2023-06-27,  发布年份 2023
来源: Springer
PDF
【 摘 要 】

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.

【 授权许可】

CC BY   
© The Author(s) 2023

【 预 览 】
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Fig. 1

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Fig. 1

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