On shrinking projection method for cutter type mappings with nonsummable errors

被引：0

作者：

Ibaraki, Takanori ^{[1
]}

Saejung, Satit ^{[2
]}

机构：

[1] Yokohama Natl Univ, Dept Math Educ, Tokiwadai,Hodogaya Ku, Yokohama 2408501, Japan

[2] Khon Kaen Univ, Fac Sci, Dept Math, Khon Kaen 40002, Thailand

来源：

JOURNAL OF INEQUALITIES AND APPLICATIONS | 2023年 / 2023卷 / 01期

关键词：

Fixed point; Shrinking projection method; Cutter type mapping; Metric projection; Generalized projection; Maximal monotone operator; PROXIMAL-TYPE ALGORITHM; NONEXPANSIVE-MAPPINGS; STRONG-CONVERGENCE; RETRACTIONS;

D O I：

10.1186/s13660-023-03004-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

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.

引用

页数：20

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