×
Schaible, S.; Yao, J. C.; Zeng, L. C.

Iterative method for set-valued mixed quasi-variational inequalities in a Banach space. (English) Zbl 1123.49006

J. Optim. Theory Appl. 129, No. 3, 425-436 (2006).
Summary: This paper introduces an iterative method for finding approximate solutions of a set-valued mixed quasivariational inequality in the setting of a Banach space. Existence of a solution of this rather general problem and the convergence of the proposed iterative method to a solution are established.

Cited in 4 Documents

MSC:

49J40 Variational inequalities
49J53 Set-valued and variational analysis
47H05 Monotone operators and generalizations
47H10 Fixed-point theorems

Keywords:

set-valued mappings; fixed-point problems; \(m\)-accretive operators; maximal monotone operators
PDF BibTeX XML Cite
\textit{S. Schaible} et al., J. Optim. Theory Appl. 129, No. 3, 425--436 (2006; Zbl 1123.49006)
Full Text: DOI
  • logo of hbz
  • logo of WorldCat

References:

[1] Adly, S., Perturbed Algorithms and Sensitivity Analysis for a General Class of Variational Inclusions, Journal of Mathematical Analysis and Applications, Vol. 201, pp. 609–630, 1996. · Zbl 0856.65077
[2] Chang, S. S., Cho, Y. J., Lee, B. S., and Jung, I. H., Generalized Set-Valued Variational Inclusions in Banach Spaces, Journal of Mathematical Analysis and Applications, Vol. 246, pp. 409–422, 2000. · Zbl 1031.49017
[3] Chang, S. S., Fuzzy Quasivariational Inclusions in Banach Spaces, Applied Mathematics and Computation, Vol. 145, pp. 805–819, 2003. · Zbl 1030.49009
[4] Ansari, Q. H., and Yao, J. C., Iterative Schemes for Solving Mixed Variational-Like Inequalities, Journal of Optimization Theory and Applications, Vol. 108, pp. 527–541, 2001. · Zbl 0999.49008
[5] Ding, X. P., Algorithm of Solutions for Mixed Implicit Quasivariational Inequalities with Fuzzy Mappings, Computers and Mathematics with Applications, Vol. 38, pp. 231–241, 1999. · Zbl 0938.49009
[6] Ding, X. P., Generalized Implicit Quasivariational Inclusions with Fuzzy Set-Valued Mappings, Computers and Mathematics with Applications, Vol. 38, pp. 71–79,1999. · Zbl 0938.49008
[7] Schaible, S., Yao, J. C., and Zeng, L. C., On the Convergence Analysis of an Iterative Algorithm for Generalized Set-Valued Variational Inclusions, Journal of Nonlinear and Convex Analysis, Vol. 5, pp. 361–368, 2004. · Zbl 1078.49008
[8] Uko, L. U., Strongly Nonlinear Generalized Equations, Journal of Mathematical Analysis and Applications, Vol. 220, pp. 65–76, 1998. · Zbl 0918.49007
[9] Zeng, L. C., Perturbed Proximal-Point Algorithm for Generalized Nonlinear Set-Valued Mixed Quasivariational Inclusions, Acta Mathematica Sinica, Vol. 47, pp. 11–18, 2004. · Zbl 1167.49304
[10] Zeng, L. C., Schaible, S., and Yao, J. C., Iterative Algorithm for Generalized Set-Valued Strongly Nonlinear Mixed Variational-Like Inequalities, Journal of Optimization Theory and Applications, Vol. 124, pp. 725–738, 2005. · Zbl 1067.49007
[11] Zeng, L. C., and Yao, J. C., On the Convergence Analysis of the Iterative Method with Errors for General Mixed Quasivariational Inequalities in Hilbert Spaces, Taiwanese Journal of Mathematics, 2006 (to appear). · Zbl 1354.49020
[12] Huang, N. J., Bai, M. R., Cho, Y. J., and Kang, S. M., Generalized Nonlinear Mixed Quasivariational Inequalities, Computers and Mathematics with Applications, Vol. 40, pp. 205–215, 2000. · Zbl 0960.47036
[13] Al-Shemas, E., and Billups, B. C., An Iterative Method for Generalized Set-Valued Nonlinear Mixed Quasivariational Inequalities, Journal of Computational and Applied Mathematics, Vol. 170, pp. 423–432, 2004. · Zbl 1060.65064
[14] Jung, J. S., and Morales, C. H., The Mann Process for Perturbed m-Accretive Operators in Banach Spaces, Nonlinear Analysis, Vol. 46, pp. 231–243,2001. · Zbl 0997.47042
[15] Barbu, V., Nonlinear Semigroups and Differential Equations in Banach Spaces,Noordhoff, Leyden, Netherlands, 1976. · Zbl 0328.47035
[16] Liu, L. W., and Li, Y. Q., On Generalized Set-Valued Variational Inclusions, Journal of Mathematical Analysis and Applications, Vol. 261, pp. 231–240, 2001. · Zbl 1070.49006
[17] Li, S. J., and Feng, D. X., The Topological Degree for Multivalued Maximal Monotone Operator in Hilbert Spaces, Acta Mathematica Sinica, Vol. 25, pp. 533–541,1982. · Zbl 0524.47040
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.