zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
General variational inequalities and nonexpansive mappings. (English) Zbl 1112.49013
Summary: We suggest and analyze some three-step iterative schemes for finding the common elements of the set of the solutions of the Noor variational inequalities involving two nonlinear operators and the set of the fixed-points of nonexpansive mappings. We also consider the convergence analysis of the suggested iterative schemes under some mild conditions. Since the Noor variational inequalities include variational inequalities and complementarity problems as special cases, results obtained in this paper continue to hold for these problems. Results obtained in this paper may be viewed as an refinement and improvement of the previously known results.

MSC:
49J40Variational methods including variational inequalities
47J20Inequalities involving nonlinear operators
WorldCat.org
Full Text: DOI
References:
[1] Ames, W. F.: Numerical methods for partial differential equations. (1992) · Zbl 0759.65059
[2] Blankenship, G. L.; Menaldi, J. L.: Optimal stochastic scheduling of power generation system with scheduling delays and large cost differentials. SIAM J. Control optim. 22, 121-132 (1984) · Zbl 0551.93076
[3] A. Bnouhachem, M. Aslam Noor, Th.M. Rassias, Three-step iterative algorithms for mixed variational inequalities, Appl. Math. Comput., in press
[4] Daniele, P.; Giannessi, F.; Maugeri, A.: Equilibrium problems and variational models. (2003) · Zbl 1030.00031
[5] Giannessi, F.; Maugeri, A.: Variational inequalities and network equilibrium problems. (1995) · Zbl 0834.00044
[6] Giannessi, F.; Maugeri, A.; Pardalos, P. M.: Equilibrium problems, nonsmooth optimization and variational inequalities problems. (2001) · Zbl 0979.00025
[7] Glowinski, R.; Lions, J. L.; Tremolieres, R.: Numerical analysis of variational inequalities. (1981) · Zbl 0463.65046
[8] Noor, M. Aslam: General variational inequalities. Appl. math. Lett. 1, 119-121 (1988) · Zbl 0655.49005
[9] Noor, M. Aslam: Wiener -- Hopf equations and variational inequalities. J. optim. Theory appl. 79, 197-206 (1993) · Zbl 0799.49010
[10] Noor, M. Aslam: Some algorithms for general monotone mixed variational inequalities. Math. comput. Modelling 29, 1-9 (1999) · Zbl 0991.49004
[11] Noor, M. A.: New approximation schemes for general variational inequalities. J. math. Anal. appl. 251, 217-229 (2000) · Zbl 0964.49007
[12] Noor, M. Aslam: New extragradient-type methods for general variational inequalities. J. math. Anal. appl. 277, 379-395 (2003) · Zbl 1033.49015
[13] Noor, M. Aslam: Some developments in general variational inequalities. Appl. math. Comput. 152, 199-277 (2004) · Zbl 1134.49304
[14] Noor, M. Aslam: Merit functions for general variational inequalities. J. math. Anal. appl. 316, 736-752 (2006) · Zbl 1085.49011
[15] Noor, M. Aslam: Projection-proximal methods for general variational inequalities. J. math. Anal. appl. 318, 53-62 (2006) · Zbl 1086.49005
[16] M. Aslam Noor, A. Bnouhachem, On an iterative algorithm for general variational inequalities, Appl. Math. Comput., in press · Zbl 1119.65058
[17] Noor, M. Aslam; Noor, K. Inayat: Self-adaptive projection algorithms for general variational inequalities. Appl. math. Comput. 151, 659-670 (2004) · Zbl 1053.65048
[18] Noor, M. Aslam; Noor, K. Inayat; Rassias, Th.M.: Some aspects of variational inequalities. J. comput. Appl. math. 47, 285-312 (1993) · Zbl 0788.65074
[19] M. Aslam Noor, Z. Huang, Three-step iterative methods for nonexpansive mappings and variational inequalities, Appl. Math. Comput. (2006), in press, doi:10.1016/j.amc.2006.08.088 · Zbl 1128.65050
[20] Patriksson, M.: Nonlinear programming and variational inequalities: A unified approach. (1998) · Zbl 0912.90261
[21] P.S.M. Santos, S. Scheimberg, A projection algorithm for general variational inequalities with perturbed constraint sets, Appl. Math. Comput., in press · Zbl 1148.65308
[22] Stampacchia, G.: Formes bilineaires coercivities sur LES ensembles convexes. C. R. Acad. sci. Paris 258, 4413-4416 (1964) · Zbl 0124.06401
[23] Takahashi, W.; Toyoda, M.: Weak convergence theorems for nonexpansive mappings and monotone mappings. J. optim. Theory appl. 118, 417-428 (2003) · Zbl 1055.47052
[24] Weng, X. L.: Fixed point iteration for local strictly pseudocontractive mappings. Proc. amer. Math. soc. 113, 727-731 (1991) · Zbl 0734.47042
[25] Xiu, N.; Zhang, J.; Noor, M. Aslam: Tangent projection equations and general variational inequalities. J. math. Anal. appl. 258, 755-762 (2001) · Zbl 1008.49010