On relaxed viscosity iterative methods for variational inequalities in Banach spaces

L. C. Ceng; Q. H. Ansari; J. C. Yao

doi:10.1016/j.cam.2009.01.015

On relaxed viscosity iterative methods for variational inequalities in Banach spaces

L. C. Ceng, Q. H. Ansari, J. C. Yao^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

20 Scopus citations

Abstract

In this paper, we suggest and analyze a relaxed viscosity iterative method for a commutative family of nonexpansive self-mappings defined on a nonempty closed convex subset of a reflexive Banach space. We prove that the sequence of approximate solutions generated by the proposed iterative algorithm converges strongly to a solution of a variational inequality. Our relaxed viscosity iterative method is an extension and variant form of the original viscosity iterative method. The results of this paper can be viewed as an improvement and generalization of the previously known results that have appeared in the literature.

Original language	English
Pages (from-to)	813-822
Number of pages	10
Journal	Journal of Computational and Applied Mathematics
Volume	230
Issue number	2
DOIs	https://doi.org/10.1016/j.cam.2009.01.015
State	Published - 15 Aug 2009
Externally published	Yes

Keywords

Common fixed points
Nonexpansive mapping
Relaxed viscosity approximation method
Strong convergence
Uniformly Gâteaux differentiable norm
Variational inequalities

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/j.cam.2009.01.015

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title = "On relaxed viscosity iterative methods for variational inequalities in Banach spaces",

abstract = "In this paper, we suggest and analyze a relaxed viscosity iterative method for a commutative family of nonexpansive self-mappings defined on a nonempty closed convex subset of a reflexive Banach space. We prove that the sequence of approximate solutions generated by the proposed iterative algorithm converges strongly to a solution of a variational inequality. Our relaxed viscosity iterative method is an extension and variant form of the original viscosity iterative method. The results of this paper can be viewed as an improvement and generalization of the previously known results that have appeared in the literature.",

keywords = "Common fixed points, Nonexpansive mapping, Relaxed viscosity approximation method, Strong convergence, Uniformly G{\^a}teaux differentiable norm, Variational inequalities",

author = "Ceng, \{L. C.\} and Ansari, \{Q. H.\} and Yao, \{J. C.\}",

year = "2009",

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doi = "10.1016/j.cam.2009.01.015",

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T1 - On relaxed viscosity iterative methods for variational inequalities in Banach spaces

AU - Ceng, L. C.

AU - Ansari, Q. H.

AU - Yao, J. C.

PY - 2009/8/15

Y1 - 2009/8/15

N2 - In this paper, we suggest and analyze a relaxed viscosity iterative method for a commutative family of nonexpansive self-mappings defined on a nonempty closed convex subset of a reflexive Banach space. We prove that the sequence of approximate solutions generated by the proposed iterative algorithm converges strongly to a solution of a variational inequality. Our relaxed viscosity iterative method is an extension and variant form of the original viscosity iterative method. The results of this paper can be viewed as an improvement and generalization of the previously known results that have appeared in the literature.

AB - In this paper, we suggest and analyze a relaxed viscosity iterative method for a commutative family of nonexpansive self-mappings defined on a nonempty closed convex subset of a reflexive Banach space. We prove that the sequence of approximate solutions generated by the proposed iterative algorithm converges strongly to a solution of a variational inequality. Our relaxed viscosity iterative method is an extension and variant form of the original viscosity iterative method. The results of this paper can be viewed as an improvement and generalization of the previously known results that have appeared in the literature.

KW - Common fixed points

KW - Nonexpansive mapping

KW - Relaxed viscosity approximation method

KW - Strong convergence

KW - Uniformly Gâteaux differentiable norm

KW - Variational inequalities

UR - https://www.scopus.com/pages/publications/67349147524

U2 - 10.1016/j.cam.2009.01.015

DO - 10.1016/j.cam.2009.01.015

M3 - Article

AN - SCOPUS:67349147524

SN - 0377-0427

VL - 230

SP - 813

EP - 822

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

IS - 2

ER -

On relaxed viscosity iterative methods for variational inequalities in Banach spaces

Abstract

Keywords

ASJC Scopus subject areas

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