Minimum-norm solution of variational inequality and fixed point problem in banach spaces

We introduce an iterative process which converges strongly to a common minimum-norm solution of a variational inequality problem for an -inverse strongly monotone mapping and a fixed point of relatively non-expansive mapping in Banach spaces. Our theorems improve and unify most of the results that h...

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Bibliographic Details
Published inOptimization Vol. 64; no. 2; pp. 453 - 471
Main Authors Zegeye, Habtu, Shahzad, Naseer, Yao, Yonghong
Format Journal Article
LanguageEnglish
Published Philadelphia Routledge 01.02.2015
Taylor & Francis LLC
Subjects
47J25
Banach space
Banach spaces
Fixed points (mathematics)
Inequalities
Iterative methods
Mapping
Mathematical functions
Monotone mappings
Nonlinearity
Operations research
Operators
Optimization
relatively asymptotically non-expansive mappings
relatively non-expansive
strong convergence
Studies
Theorems
variational inequality problems
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Summary:We introduce an iterative process which converges strongly to a common minimum-norm solution of a variational inequality problem for an -inverse strongly monotone mapping and a fixed point of relatively non-expansive mapping in Banach spaces. Our theorems improve and unify most of the results that have been proved for this important class of non-linear operators.
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ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2013.764522