Some Algorithms for Finding Fixed Points and Solutions of Variational Inequalities | Zendy

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Some Algorithms for Finding Fixed Points and Solutions of Variational Inequalities

Author(s) -

Jong Soo Jung

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 - 10.1155/2012/153456

Subject(s) - variational inequality , mathematics , fixed point , monotone polygon , hilbert space , convergence (economics) , norm (philosophy) , operator (biology) , set (abstract data type) , discrete mathematics , algorithm , pure mathematics , mathematical analysis , computer science , geometry , biochemistry , chemistry , repressor , political science , transcription factor , law , economics , gene , programming language , economic growth

We introduce new implicit and explicit algorithms for finding the fixed point of a k-strictly pseudocontractive mapping and for solving variational inequalities related to the Lipschitzian and strongly monotone operator in Hilbert spaces. We establish results on the strong convergence of the sequences generated by the proposed algorithms to a fixed point of a k-strictly pseudocontractive mapping. Such a point is also a solution of a variational inequality defined on the set of fixed points. As direct consequences, we obtain the unique minimum-norm fixed point of a k-strictly pseudocontractive mapping

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