Abstract and Applied Analysis

Iterative methods for solving fixed-point problems with nonself-mappings in Banach spaces

Yakov Alber, Simeon Reich, and Jen-Chih Yao

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Abstract

We study descent-like approximation methods and proximal methods of the retraction type for solving fixed-point problems with nonself-mappings in Hilbert and Banach spaces. We prove strong and weak convergences for weakly contractive and nonexpansive maps, respectively. We also establish the stability of these methods with respect to perturbations of the operators and the constraint sets.

Article information

Source
Abstr. Appl. Anal., Volume 2003, Number 4 (2003), 193-216.

Dates
First available in Project Euclid: 15 April 2003

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1050426015

Digital Object Identifier
doi:10.1155/S1085337503203018

Mathematical Reviews number (MathSciNet)
MR1982091

Zentralblatt MATH identifier
1028.47049

Subjects
Primary: 47H06: Accretive operators, dissipative operators, etc. 47H09
Secondary: 47H10 47H14 49M25

Citation

Alber, Yakov; Reich, Simeon; Yao, Jen-Chih. Iterative methods for solving fixed-point problems with nonself-mappings in Banach spaces. Abstr. Appl. Anal. 2003 (2003), no. 4, 193--216. doi:10.1155/S1085337503203018. https://projecteuclid.org/euclid.aaa/1050426015


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