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)
Generalized nonlinear mixed quasi-variational inequalities. (English) Zbl 0960.47036

The problem is studied to find in a Hilbert space u, xSu, yTu, and zGu such that the inclusion 0N(x,y)+M(p(u),z) holds. Here, M(·,z) is assumed to be maximal monotone where the resolvent (I+ρM(·,z)) -1 is Lipschitz with respect to z; S,T,G are Lipschitz with respect to the Hausdorff distance, and for p and N Lipschitz and monotonicity conditions are assumed (always with appropriate constants).

An iterative algorithm is suggested whose convergence to a solution is proved. Moreover, for single-valued S,T and G=I also stability of a perturbed algorithm is proved.


MSC:
47J20Inequalities involving nonlinear operators
47J25Iterative procedures (nonlinear operator equations)
47H05Monotone operators (with respect to duality) and generalizations
49J40Variational methods including variational inequalities