Systems of Variational Inequalities with Nonlinear Operators

In this work, we concern ourselves with the problem of solving a general system of variational inequalities whose solutions also solve a common fixed-point problem of a family of countably many nonlinear operators via a hybrid viscosity implicit iteration method in 2 uniformly smooth and uniformly c...

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Main Authors:	Lu-Chuan Ceng, Qing Yuan
Format:	Article
Language:	English
Published:	MDPI AG 2019-04-01
Series:	Mathematics
Subjects:	implicit iterations variational inequalities lipschitzian pseudocontractions asymptotically nonexpansive mapping fixed-point banach space
Online Access:	https://www.mdpi.com/2227-7390/7/4/338

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spelling	doaj-c2aff2de3ad34bdfaba3dc5a642e3ac62020-11-25T01:56:26ZengMDPI AGMathematics2227-73902019-04-017433810.3390/math7040338math7040338Systems of Variational Inequalities with Nonlinear OperatorsLu-Chuan Ceng0Qing Yuan1Department of Mathematics, Shanghai Normal University, Shanghai 200234, ChinaSchool of Mathematics and Statistics, Linyi University, Linyi 276000, ChinaIn this work, we concern ourselves with the problem of solving a general system of variational inequalities whose solutions also solve a common fixed-point problem of a family of countably many nonlinear operators via a hybrid viscosity implicit iteration method in 2 uniformly smooth and uniformly convex Banach spaces. An application to common fixed-point problems of asymptotically nonexpansive and pseudocontractive mappings and variational inequality problems for strict pseudocontractive mappings is also given in Banach spaces.https://www.mdpi.com/2227-7390/7/4/338implicit iterationsvariational inequalitieslipschitzian pseudocontractionsasymptotically nonexpansive mappingfixed-pointbanach space
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Lu-Chuan Ceng Qing Yuan
spellingShingle	Lu-Chuan Ceng Qing Yuan Systems of Variational Inequalities with Nonlinear Operators Mathematics implicit iterations variational inequalities lipschitzian pseudocontractions asymptotically nonexpansive mapping fixed-point banach space
author_facet	Lu-Chuan Ceng Qing Yuan
author_sort	Lu-Chuan Ceng
title	Systems of Variational Inequalities with Nonlinear Operators
title_short	Systems of Variational Inequalities with Nonlinear Operators
title_full	Systems of Variational Inequalities with Nonlinear Operators
title_fullStr	Systems of Variational Inequalities with Nonlinear Operators
title_full_unstemmed	Systems of Variational Inequalities with Nonlinear Operators
title_sort	systems of variational inequalities with nonlinear operators
publisher	MDPI AG
series	Mathematics
issn	2227-7390
publishDate	2019-04-01
description	In this work, we concern ourselves with the problem of solving a general system of variational inequalities whose solutions also solve a common fixed-point problem of a family of countably many nonlinear operators via a hybrid viscosity implicit iteration method in 2 uniformly smooth and uniformly convex Banach spaces. An application to common fixed-point problems of asymptotically nonexpansive and pseudocontractive mappings and variational inequality problems for strict pseudocontractive mappings is also given in Banach spaces.
topic	implicit iterations variational inequalities lipschitzian pseudocontractions asymptotically nonexpansive mapping fixed-point banach space
url	https://www.mdpi.com/2227-7390/7/4/338
work_keys_str_mv	AT luchuanceng systemsofvariationalinequalitieswithnonlinearoperators AT qingyuan systemsofvariationalinequalitieswithnonlinearoperators
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Systems of Variational Inequalities with Nonlinear Operators

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