Strong Convergence of Viscosity Iteration Methods for Nonexpansive Mappings | Zendy

Jong Soo Jung | Zendy

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Strong Convergence of Viscosity Iteration Methods for Nonexpansive Mappings

Author(s) -

Jong Soo Jung

Publication year - 2009

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 - 10.1155/2009/573156

Subject(s) - mathematics , variational inequality , banach space , differentiable function , fixed point , viscosity , convergence (economics) , norm (philosophy) , regular polygon , iterative method , scheme (mathematics) , mathematical analysis , mathematical optimization , geometry , physics , quantum mechanics , political science , law , economics , economic growth

We propose a new viscosity iterative scheme for finding fixed points of nonexpansive mappingsin a reflexive Banach space having a uniformly Gâteaux differentiable norm and satisfying that every weakly compact convex subset of the space has the fixed point property for nonexpansive mappings. Certain different control conditions for viscosity iterative scheme are given and strong convergence of viscosity iterativescheme to a solution of a ceratin variational inequality is established

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