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)
Existence of solutions for a system of generalized nonlinear implicit variational inequalities. (English) Zbl 1078.47034
Let H be a real Hilbert space with inner product ·,·. Let ξ,η be elements of H, ρ and β be positive constants, and K a nonempty closed convex subset of H. Let f,g,N:HH and M:H×HH be nonlinear mappings with Kg(H). The paper is concerned with the following problem: find x,yH such that f(x),g(y)K and ρ(M(x,g(y))-ξ)+f(x)-g(y),v-f(x)0, β(N(x)-η)+g(y)-f(x),v-g(y)0, vK. The authors construct an iterative algorithm for the problem and establish strong convergence of the algorithm under appropriate monotonicity and continuity conditions on the operators.
MSC:
47J20Inequalities involving nonlinear operators
49J40Variational methods including variational inequalities