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Erschienen in: Journal of Inequalities and Applications 1/2006

Open Access 01.12.2006 | Research Article

Iterative algorithm for solving mixed quasi-variational-like inequalities with skew-symmetric terms in Banach spaces

verfasst von: Lu-Chuan Ceng, Qamrul Hasan Ansari, Jen-Chih Yao

Erschienen in: Journal of Inequalities and Applications | Ausgabe 1/2006

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Abstract

We develop an iterative algorithm for computing the approximate solutions of mixed quasi-variational-like inequality problems with skew-symmetric terms in the setting of reflexive Banach spaces. We use Fan-KKM lemma and concept of https://static-content.springer.com/image/art%3A10.1155%2FJIA%2F2006%2F82695/MediaObjects/13660_2006_Article_1645_IEq1_HTML.gif -cocoercivity of a composition mapping to prove the existence and convergence of approximate solutions to the exact solution of mixed quasi-variational-like inequalities with skew-symmetric terms. Furthermore, we derive the posteriori error estimates for approximate solutions under quite mild conditions.

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Literatur
1.
Zurück zum Zitat Ansari QH, Yao J-C: Iterative schemes for solving mixed variational-like inequalities. Journal of Optimization Theory and Applications 2001,108(3):527–541. 10.1023/A:1017531323904MathSciNetCrossRefMATH Ansari QH, Yao J-C: Iterative schemes for solving mixed variational-like inequalities. Journal of Optimization Theory and Applications 2001,108(3):527–541. 10.1023/A:1017531323904MathSciNetCrossRefMATH
2.
Zurück zum Zitat Antipin AS: Iterative gradient prediction-type methods for computing fixed points of extremal mapping. In Parametric Optimization and Related Topics, IV (Enschede, 1995), Approx. Optim.. Volume 9. Edited by: Guddat J, Jonden HTh, Nizicka F, Still G, Twitt F. Lang, Frankfurt am Main; 1997:11–24. Antipin AS: Iterative gradient prediction-type methods for computing fixed points of extremal mapping. In Parametric Optimization and Related Topics, IV (Enschede, 1995), Approx. Optim.. Volume 9. Edited by: Guddat J, Jonden HTh, Nizicka F, Still G, Twitt F. Lang, Frankfurt am Main; 1997:11–24.
3.
Zurück zum Zitat Dien NH: Some remarks on variational-like and quasivariational-like inequalities. Bulletin of the Australian Mathematical Society 1992,46(2):335–342. 10.1017/S0004972700011941MathSciNetCrossRefMATH Dien NH: Some remarks on variational-like and quasivariational-like inequalities. Bulletin of the Australian Mathematical Society 1992,46(2):335–342. 10.1017/S0004972700011941MathSciNetCrossRefMATH
4.
Zurück zum Zitat Ding XP, Yao J-C: Existence and algorithm of solutions for mixed quasi-variational-like inclusions in Banach spaces. Computers & Mathematics with Applications 2005,49(5–6):857–869. 10.1016/j.camwa.2004.05.013MathSciNetCrossRefMATH Ding XP, Yao J-C: Existence and algorithm of solutions for mixed quasi-variational-like inclusions in Banach spaces. Computers & Mathematics with Applications 2005,49(5–6):857–869. 10.1016/j.camwa.2004.05.013MathSciNetCrossRefMATH
5.
6.
Zurück zum Zitat Glowinski R, Lions J-L, Trémolières R: Numerical Analysis of Variational Inequalities, Studies in Mathematics and Its Applications. Volume 8. North-Holland, Amsterdam; 1981:xxix+776. Glowinski R, Lions J-L, Trémolières R: Numerical Analysis of Variational Inequalities, Studies in Mathematics and Its Applications. Volume 8. North-Holland, Amsterdam; 1981:xxix+776.
7.
Zurück zum Zitat Hanson MA: On sufficiency of the Kuhn-Tucker conditions. Journal of Mathematical Analysis and Applications 1981,80(2):545–550. 10.1016/0022-247X(81)90123-2MathSciNetCrossRefMATH Hanson MA: On sufficiency of the Kuhn-Tucker conditions. Journal of Mathematical Analysis and Applications 1981,80(2):545–550. 10.1016/0022-247X(81)90123-2MathSciNetCrossRefMATH
8.
Zurück zum Zitat Huang N-J, Deng C-X: Auxiliary principle and iterative algorithms for generalized set-valued strongly nonlinear mixed variational-like inequalities. Journal of Mathematical Analysis and Applications 2001,256(2):345–359. 10.1006/jmaa.2000.6988MathSciNetCrossRefMATH Huang N-J, Deng C-X: Auxiliary principle and iterative algorithms for generalized set-valued strongly nonlinear mixed variational-like inequalities. Journal of Mathematical Analysis and Applications 2001,256(2):345–359. 10.1006/jmaa.2000.6988MathSciNetCrossRefMATH
9.
Zurück zum Zitat Karamardian S: The nonlinear complementarity problem with applications. II. Journal of Optimization Theory and Applications 1969,4(3):167–181. 10.1007/BF00930577MathSciNetCrossRefMATH Karamardian S: The nonlinear complementarity problem with applications. II. Journal of Optimization Theory and Applications 1969,4(3):167–181. 10.1007/BF00930577MathSciNetCrossRefMATH
10.
Zurück zum Zitat Lee C-H, Ansari QH, Yao J-C: A perturbed algorithm for strongly nonlinear variational-like inclusions. Bulletin of the Australian Mathematical Society 2000,62(3):417–426. 10.1017/S0004972700018931MathSciNetCrossRefMATH Lee C-H, Ansari QH, Yao J-C: A perturbed algorithm for strongly nonlinear variational-like inclusions. Bulletin of the Australian Mathematical Society 2000,62(3):417–426. 10.1017/S0004972700018931MathSciNetCrossRefMATH
12.
Zurück zum Zitat Siddiqi AH, Ansari QH, Ahmad R: Some remarks on variational-like inequalities. In Mathematics and Its Applications in Industry and Business. Edited by: Siddiqi AH, Ahmad K. Narosa, New Delhi; 2000:101–108. Siddiqi AH, Ansari QH, Ahmad R: Some remarks on variational-like inequalities. In Mathematics and Its Applications in Industry and Business. Edited by: Siddiqi AH, Ahmad K. Narosa, New Delhi; 2000:101–108.
13.
Zurück zum Zitat Tseng P: Further applications of a splitting algorithm to decomposition in variational inequalities and convex programming. Mathematical Programming, Series B 1990,48(2):249–263.CrossRefMathSciNetMATH Tseng P: Further applications of a splitting algorithm to decomposition in variational inequalities and convex programming. Mathematical Programming, Series B 1990,48(2):249–263.CrossRefMathSciNetMATH
14.
Zurück zum Zitat Zeng L-C: Iterative algorithm for finding approximate solutions of a class of mixed variational-like inequalities. Acta Mathematicae Applicatae Sinica. English Series 2004,20(3):477–486. 10.1007/s10255-004-0185-8MathSciNetCrossRefMATH Zeng L-C: Iterative algorithm for finding approximate solutions of a class of mixed variational-like inequalities. Acta Mathematicae Applicatae Sinica. English Series 2004,20(3):477–486. 10.1007/s10255-004-0185-8MathSciNetCrossRefMATH
15.
Zurück zum Zitat Zeng LC: Iterative approximation of solutions to generalized set-valued strongly nonlinear mixed variational-like inequalities. Acta Mathematica Sinica (Chinese Series) 2005,48(5):879–888.MathSciNetMATH Zeng LC: Iterative approximation of solutions to generalized set-valued strongly nonlinear mixed variational-like inequalities. Acta Mathematica Sinica (Chinese Series) 2005,48(5):879–888.MathSciNetMATH
16.
Zurück zum Zitat Zeng LC, Schaible S, Yao J-C: Iterative algorithm for generalized set-valued strongly nonlinear mixed variational-like inequalities. Journal of Optimization Theory and Applications 2005,124(3):725–738. 10.1007/s10957-004-1182-zMathSciNetCrossRefMATH Zeng LC, Schaible S, Yao J-C: Iterative algorithm for generalized set-valued strongly nonlinear mixed variational-like inequalities. Journal of Optimization Theory and Applications 2005,124(3):725–738. 10.1007/s10957-004-1182-zMathSciNetCrossRefMATH
17.
Zurück zum Zitat Zhu DL, Marcotte P: Co-coercivity and its role in the convergence of iterative schemes for solving variational inequalities. SIAM Journal on Optimization 1996,6(3):714–726. 10.1137/S1052623494250415MathSciNetCrossRefMATH Zhu DL, Marcotte P: Co-coercivity and its role in the convergence of iterative schemes for solving variational inequalities. SIAM Journal on Optimization 1996,6(3):714–726. 10.1137/S1052623494250415MathSciNetCrossRefMATH
Metadaten
Titel
Iterative algorithm for solving mixed quasi-variational-like inequalities with skew-symmetric terms in Banach spaces
verfasst von
Lu-Chuan Ceng
Qamrul Hasan Ansari
Jen-Chih Yao
Publikationsdatum
01.12.2006
Verlag
Springer International Publishing
Erschienen in
Journal of Inequalities and Applications / Ausgabe 1/2006
Elektronische ISSN: 1029-242X
DOI
https://doi.org/10.1155/JIA/2006/82695

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