Strong Convergence of a Unified General Iteration for k-Strictly Pseudononspreading Mapping in Hilbert Spaces

Strong Convergence of a Unified General Iteration for k-Strictly Pseudononspreading Mapping in Hilbert Spaces

We introduce a unified general iterative method to approximate a fixed point of k-strictly pseudononspreading mapping. Under some suitable conditions, we prove that the iterative sequence generated by the proposed method converges strongly to a fixed point of a k-strictly pseudononspreading mapping...

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Main Authors: Dao-Jun Wen, Yi-An Chen, Yan Tang
Format: Article
Language:English
Published: Hindawi Limited 2014-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2014/219695
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spelling doaj-e40099b186d446ada61f9d8974db90212020-11-24T21:14:48ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/219695219695Strong Convergence of a Unified General Iteration for k-Strictly Pseudononspreading Mapping in Hilbert SpacesDao-Jun Wen0Yi-An Chen1Yan Tang2College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, ChinaCollege of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, ChinaCollege of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, ChinaWe introduce a unified general iterative method to approximate a fixed point of k-strictly pseudononspreading mapping. Under some suitable conditions, we prove that the iterative sequence generated by the proposed method converges strongly to a fixed point of a k-strictly pseudononspreading mapping with an idea of mean convergence, which also solves a class of variational inequalities as an optimality condition for a minimization problem. The results presented in this paper may be viewed as a refinement and as important generalizations of the previously known results announced by many other authors.http://dx.doi.org/10.1155/2014/219695
collection DOAJ
language English
format Article
sources DOAJ
author Dao-Jun Wen
Yi-An Chen
Yan Tang
spellingShingle Dao-Jun Wen
Yi-An Chen
Yan Tang
Strong Convergence of a Unified General Iteration for k-Strictly Pseudononspreading Mapping in Hilbert Spaces
Abstract and Applied Analysis
author_facet Dao-Jun Wen
Yi-An Chen
Yan Tang
author_sort Dao-Jun Wen
title Strong Convergence of a Unified General Iteration for k-Strictly Pseudononspreading Mapping in Hilbert Spaces
title_short Strong Convergence of a Unified General Iteration for k-Strictly Pseudononspreading Mapping in Hilbert Spaces
title_full Strong Convergence of a Unified General Iteration for k-Strictly Pseudononspreading Mapping in Hilbert Spaces
title_fullStr Strong Convergence of a Unified General Iteration for k-Strictly Pseudononspreading Mapping in Hilbert Spaces
title_full_unstemmed Strong Convergence of a Unified General Iteration for k-Strictly Pseudononspreading Mapping in Hilbert Spaces
title_sort strong convergence of a unified general iteration for k-strictly pseudononspreading mapping in hilbert spaces
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2014-01-01
description We introduce a unified general iterative method to approximate a fixed point of k-strictly pseudononspreading mapping. Under some suitable conditions, we prove that the iterative sequence generated by the proposed method converges strongly to a fixed point of a k-strictly pseudononspreading mapping with an idea of mean convergence, which also solves a class of variational inequalities as an optimality condition for a minimization problem. The results presented in this paper may be viewed as a refinement and as important generalizations of the previously known results announced by many other authors.
url http://dx.doi.org/10.1155/2014/219695
work_keys_str_mv AT daojunwen strongconvergenceofaunifiedgeneraliterationforkstrictlypseudononspreadingmappinginhilbertspaces
AT yianchen strongconvergenceofaunifiedgeneraliterationforkstrictlypseudononspreadingmappinginhilbertspaces
AT yantang strongconvergenceofaunifiedgeneraliterationforkstrictlypseudononspreadingmappinginhilbertspaces
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