Abstract and Applied Analysis

Hybrid Algorithm of Fixed Point for Weak Relatively Nonexpansive Multivalued Mappings and Applications

Jingling Zhang, Yongfu Su, and Qingqing Cheng

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Abstract

The purpose of this paper is to present the notion of weak relatively nonexpansive multi-valued mapping and to prove the strong convergence theorems of fixed point for weak relatively nonexpansive multivalued mappings in Banach spaces. The weak relatively nonexpansive multivalued mappings are more generalized than relatively nonexpansive multivalued mappings. In this paper, an example will be given which is a weak relatively nonexpansive multivalued mapping but not a relatively nonexpansive multivalued mapping. In order to get the strong convergence theorems for weak relatively nonexpansive multivalued mappings, a new monotone hybrid iteration algorithm with generalized (metric) projection is presented and is used to approximate the fixed point of weak relatively nonexpansive multivalued mappings. In this paper, the notion of multivalued resolvent of maximal monotone operator has been also presented which is a weak relatively nonexpansive multivalued mapping and can be used to find the zero point of maximal monotone operator.

Article information

Source
Abstr. Appl. Anal., Volume 2012 (2012), Article ID 479438, 13 pages.

Dates
First available in Project Euclid: 28 March 2013

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1364475932

Digital Object Identifier
doi:10.1155/2012/479438

Mathematical Reviews number (MathSciNet)
MR2994962

Zentralblatt MATH identifier
1256.47059

Citation

Zhang, Jingling; Su, Yongfu; Cheng, Qingqing. Hybrid Algorithm of Fixed Point for Weak Relatively Nonexpansive Multivalued Mappings and Applications. Abstr. Appl. Anal. 2012 (2012), Article ID 479438, 13 pages. doi:10.1155/2012/479438. https://projecteuclid.org/euclid.aaa/1364475932


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