# 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)
Viscosity approximation methods for strongly positive and monotone operators. (English) Zbl 1196.47044

The purpose of this paper is to suggest and analyze both explicit and implicit iterative schemes for two strongly positive operators and a nonexpansive mapping $S$ on a Hilbert space, and to study explicit and implicit versions of iterative schemes for an inverse-strongly monotone mapping $T$ and $S$ by an extragradient-like approximation method. The viscosity approximation methods are employed to establish strong convergence of the iterative schemes to a common element of the set of fixed points of $S$ and the set of solutions of the variational inequality for $T$. Further, some applications of finding a common fixed point of a nonexpansive mapping and a strictly pseudocontractive mapping which solves some variational inequalities are given.

The results presented in this paper improve and unify various results about viscosity approximation methods for fixed-point problems and variational inequality problems.

##### MSC:
 47J25 Iterative procedures (nonlinear operator equations) 47J20 Inequalities involving nonlinear operators 49J40 Variational methods including variational inequalities 90C31 Sensitivity, stability, parametric optimization