Hybrid Algorithm of Fixed Point for Weak Relatively NonexpansiveMultivalued Mappings and Applications | Zendy

Jingling Zhang | Zendy; Yongfu Su | Zendy; Qingqing Cheng | Zendy

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Hybrid Algorithm of Fixed Point for Weak Relatively NonexpansiveMultivalued Mappings and Applications

Author(s) -

Jingling Zhang,

Yongfu Su,

Qingqing Cheng

Publication year - 2012

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2012/479438

Subject(s) - mathematics , monotone polygon , fixed point , resolvent , convergence (economics) , banach space , weak convergence , projection (relational algebra) , monotonic function , operator (biology) , pure mathematics , discrete mathematics , algorithm , mathematical analysis , computer science , geometry , biochemistry , chemistry , computer security , repressor , transcription factor , economics , asset (computer security) , gene , economic growth

The purpose of this paper is to present the notion of weak relativelynonexpansive 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

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