In this paper, we propose an explicit viscosity approximation method for finding a common element of the set of fixed points of strict pseudo-contractions and of the set of solutions of variational inequalities with inverse-strongly monotone mappings. Strong convergence theorems are established in the framework of Hilbert spaces. 2000 Mathematics Subject Classification: 47H05, 47H09, 47J25

Abstract We introduce a dynamical system to the problem of finding zeros sum two maximally monotone operators. investigate existence, uniqueness and extendability solutions this in Hilbert space. prove that trajectories proposed converge strongly primal–dual solution considered problem. Under explicit time discretization we obtain best approximation algorithm for solving coupled inclusion

In this paper, a new three-step iterative scheme is introduced for finding the common element of the set of fixed points of a nonexpansive mapping and the set of solutions of a variational inequality for α-inverse-strongly monotone mappings. The result reveals that the proposed iterative sequence converges strongly to the common element of this two. And our studies can be regarded as an extensi...

The purpose of this paper is to introduce a general iterative process for the problem of finding a common element in the set of common fixed points of an infinite family of nonexpansive mappings and in the set of solutions of variational inequalities for inverse-strongly monotone mappings.

For a maximal monotone operator T on a Hilbert space H and a closed subspace A of H, we consider the problem of finding (x, y ∈ T (x)) satisfying x ∈ A and y ∈ A⊥. An equivalent formulation of this problem makes use of the partial inverse operator of Spingarn. The resulting generalized equation can be solved by using the proximal point algorithm. We consider instead the use of hybrid proximal m...

The proximal point methods have been widely used in the last decades to approximate the solutions of nonlinear equations associated with monotone operators. Inspired by the iterative procedure defined by B. Martinet (1970), R.T. Rockafellar introduced in 1976 the so-called proximal point algorithm (PPA) for a general maximal monotone operator. The sequence generated by this iterative method is ...

We use representations of maximal monotone operators for studying recession (or asymptotic) operators associated to maximal monotone operators. Such a concept is useful for dealing with unboundedness. Dedicated to Alfred Auslender on the occasion of his sixty-fifth birthday

We introduce an iterative method for finding a common element of set of fixed points of nonexpansive mappings, the set of solutions of a finite family of variational inclusion with setvalued maximal monotone mappings and inverse strongly monotone mappings, and the set of solutions of a mixed equilibrium problem in Hilbert spaces. Under suitable conditions, some strong convergence theorems for a...