Implicit iterative method for hierarchical variational inequalities

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

doi:10.1155/2012/472935

Implicit iterative method for hierarchical variational inequalities

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

^*Corresponding author for this work

King Fahd University of Petroleum & Minerals

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

6 Scopus citations

Abstract

We introduce a new implicit iterative scheme with perturbation for finding the approximate solutions of a hierarchical variational inequality, that is, a variational inequality over the common fixed point set of a finite family of nonexpansive mappings. We establish some convergence theorems for the sequence generated by the proposed implicit iterative scheme. In particular, necessary and sufficient conditions for the strong convergence of the sequence are obtained.

Original language	English
Article number	472935
Journal	Journal of Applied Mathematics
Volume	2012
DOIs	https://doi.org/10.1155/2012/472935
State	Published - 2012

ASJC Scopus subject areas

Applied Mathematics

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title = "Implicit iterative method for hierarchical variational inequalities",

abstract = "We introduce a new implicit iterative scheme with perturbation for finding the approximate solutions of a hierarchical variational inequality, that is, a variational inequality over the common fixed point set of a finite family of nonexpansive mappings. We establish some convergence theorems for the sequence generated by the proposed implicit iterative scheme. In particular, necessary and sufficient conditions for the strong convergence of the sequence are obtained.",

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

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T1 - Implicit iterative method for hierarchical variational inequalities

AU - Ceng, L. C.

AU - Ansari, Q. H.

AU - Wong, N. C.

AU - Yao, J. C.

PY - 2012

Y1 - 2012

N2 - We introduce a new implicit iterative scheme with perturbation for finding the approximate solutions of a hierarchical variational inequality, that is, a variational inequality over the common fixed point set of a finite family of nonexpansive mappings. We establish some convergence theorems for the sequence generated by the proposed implicit iterative scheme. In particular, necessary and sufficient conditions for the strong convergence of the sequence are obtained.

AB - We introduce a new implicit iterative scheme with perturbation for finding the approximate solutions of a hierarchical variational inequality, that is, a variational inequality over the common fixed point set of a finite family of nonexpansive mappings. We establish some convergence theorems for the sequence generated by the proposed implicit iterative scheme. In particular, necessary and sufficient conditions for the strong convergence of the sequence are obtained.

UR - https://www.scopus.com/pages/publications/84861018507

U2 - 10.1155/2012/472935

DO - 10.1155/2012/472935

M3 - Article

AN - SCOPUS:84861018507

SN - 1110-757X

VL - 2012

JO - Journal of Applied Mathematics

JF - Journal of Applied Mathematics

M1 - 472935

ER -

Implicit iterative method for hierarchical variational inequalities

Abstract

ASJC Scopus subject areas

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