Weak and Strong Convergence Theorems for Zeroes of Accretive Operators in Banach Spaces | Zendy

Yanlai Song | Zendy; Lu-Chuan Ceng | Zendy

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Weak and Strong Convergence Theorems for Zeroes of Accretive Operators in Banach Spaces

Author(s) -

Yanlai Song,

Lu-Chuan Ceng

Publication year - 2014

Publication title -

journal of applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.307

H-Index - 43

eISSN - 1687-0042

pISSN - 1110-757X

DOI - 10.1155/2014/943753

Subject(s) - banach space , mathematics , convergence (economics) , weak convergence , extension (predicate logic) , set (abstract data type) , pure mathematics , fixed point , mathematical analysis , computer science , computer security , economics , asset (computer security) , programming language , economic growth

The purpose of this paper is to present two new forward-backward splitting schemes with relaxations and errors for finding a common element of the set of solutions to the variational inclusion problem with two accretive operators and the set of fixed points of nonexpansive mappings in infinite-dimensional Banach spaces. Under mild conditions, some weak and strong convergence theorems for approximating this common elements are proved. The methods in the paper are novel and different from those in the early and recent literature. Our results can be viewed as the improvement, supplementation, development, and extension of the corresponding results in the very recent literature

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