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)
Three-step iterations for variational inequalities and nonexpansive mappings. (English) Zbl 1128.65051
The authors propose a new three-step iterative method for finding the common elements of the variational inequalities and the fixed points of the nonexpansive mappings. They also consider the convergence analysis of the new method for the strongly inverse co-coercive mappings. The results proved in this paper may be viewed as an important improvement of the previously known results. They are to some extent general in nature and may stimulate the topic of research.

MSC:
65K10Optimization techniques (numerical methods)
49J40Variational methods including variational inequalities
WorldCat.org
Full Text: DOI
References:
[1] Bnouhachem, A.; Noor, M. Aslam; Rassias, Th. M.: Three-steps iterative algorithms for mixed variational inequalities. Appl. math. Comput. 183, 436-446 (2006) · Zbl 1111.65058
[2] Browder, F. E.; Petryshyn, W. V.: Construction of fixed points of nonlinear mappings in Hilbert spaces. J. math. Anal. appl. 20, 197-228 (1967) · Zbl 0153.45701
[3] Liu, F.; Nashed, M. Z.: Regularization of nonlinear ill-posed variational inequalities and convergence rates. Set-valued anal. 6, 313-344 (1998) · Zbl 0924.49009
[4] Takahashi, W.: Nonlinear functional analysis. (2000) · Zbl 0997.47002
[5] Takahashi, W.; Toyoda, M.: Weak convergence theorems for nonexpansive mappings and monotone mappings. J. optim. Theory appl. 118, 417-428 (2003) · Zbl 1055.47052
[6] Noor, M. Aslam: Some algorithms for general monotone variational inequalities. Math. comput. Model. 29, 1-9 (1999) · Zbl 0991.49004
[7] Noor, M. Aslam: New approximation schemes for general variational inequalities. J. math. Anal. appl. 251, 217-229 (2000) · Zbl 0964.49007
[8] Noor, M. Aslam: Some developments in general variational inequalities. Appl. math. Comput., 191-277 (2004) · Zbl 1134.49304
[9] M. Aslam Noor, General variational inequalities and nonexpansive mappings, J. Math. Anal. Appl., in press, doi:10.1016/j.jmaa.2006.09.039. · Zbl 1112.49013
[10] M. Aslam Noor, Z. Huang, Three-step methods for nonexpansive mappings and variational inequalities, Appl. Math. Comput., in press, doi:10.1016/j.amc.2006.08.088. · Zbl 1128.65050
[11] Noor, M. Aslam; Bnouhachem, A.: On an iterative algorithm for general variational inequalities. Appl. math. Comput. 185, 155-168 (2007) · Zbl 1119.65058
[12] Osilike, M. O.: Weak and strong convergence theorems for fixed points of pseudocontractions and solutions of monotone type operator equations. Comput. math. Appl. 40, 559-567 (2000) · Zbl 0958.47030
[13] Suzuki, T.: Strong convergence of Krasnoselskii and Mann’s type sequences for one-parameter nonexpansive semigroups without Bochner integrals. J. math. Anal. appl. 305, 227-239 (2005) · Zbl 1068.47085
[14] Xu, H. K.: Viscosity approximation methods for nonexpansive mappings. J. math. Anal. appl. 298, 279-291 (2004) · Zbl 1061.47060
[15] Y. Yao, J.C. Yao, On modified iterative method for nonexpansive mappings and monotone mappings, Appl. Math. Comput., in press, doi:10.1016/j.amc.2006.08.062. · Zbl 1121.65064