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Convergence theorems for fixed point problems and variational inequality problems in Hilbert spaces
Author(s) -
Yao Yonghong,
Liou YeongCheng,
Chen Rudong
Publication year - 2009
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200610817
Subject(s) - mathematics , variational inequality , hilbert space , monotone polygon , convergence (economics) , fixed point , sequence (biology) , strongly monotone , scheme (mathematics) , inverse , element (criminal law) , set (abstract data type) , pure mathematics , mathematical analysis , geometry , computer science , biology , political science , economic growth , law , economics , genetics , programming language
Abstract In this paper, we introduce an iterative scheme for finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality for an α ‐inverse strongly monotone mapping in a Hilbert space. We show that the sequence converges strongly to a common element of two sets under some mild conditions on parameters (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)