Open AccessGeneralized Systems of Variational Inequalities and Projection Methods for Inverse-Strongly Monotone Mappings
Author(s) -
Wiyada Kumam,
Prapairat Junlouchai,
Poom Kumam
Publication year - 2011
Publication title -
discrete dynamics in nature and society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.264
H-Index - 39
eISSN - 1607-887X
pISSN - 1026-0226
DOI - 10.1155/2011/976505
Subject(s) - variational inequality , hilbert space , monotone polygon , strongly monotone , mathematics , convergence (economics) , sequence (biology) , projection (relational algebra) , inverse , fixed point , monotonic function , operator (biology) , set (abstract data type) , pure mathematics , mathematical analysis , algorithm , computer science , biochemistry , chemistry , geometry , repressor , biology , gene , transcription factor , economics , genetics , programming language , economic growth
We introduce an iterative sequence for finding a common element of the set of fixed points of a nonexpansive mapping and the solutions of the variational inequality problem for three inverse-strongly monotonemappings. Under suitable conditions, some strong convergence theorems for approximating a common element of the above two sets are obtained. Moreover, using the above theorem, we also apply to find solutions of a general system of variational inequality and a zero of a maximal monotone operator in a real Hilbert space. As applications, at the end of the paper we utilize our results to study some convergence problem for strictly pseudocontractive mappings. Our results include the previous results as special cases extend and improve the results of Ceng et al., (2008) and many others
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