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 ...

In this paper, we introduce a new iterative scheme for finding the common element of the set of common fixed points of infinitely many nonexpansive mappings, the set of solutions of an equilibrium problem and the set of solutions of a general system of variational inequalities for inverse-strongly monotone mappings in Hilbert spaces. We prove that the sequence converges strongly to a common ele...

In this paper, we investigate the split variational inequality problem in Hilbert spaces, which an operator is ?-inverse strongly ?-monotone and another pseudomonotone. We construct iterative algorithm for solving problem. show strong convergence of suggested algorithm.

In this paper, we introduce an iterative process which converges strongly to a common element of solutions of variational inequality problems for γ-inverse strongly monotone mappings and common fixed points of a countable family of total quasi-φ-asymptotically nonexpansive nonself mappings, and hence obtain related convergence theorems in Banach spaces. Mathematics Subject Classification: 47H09...

For a simple drawing D of the complete graph $$K_n$$ , two (plane) subdrawings are compatible if their union is plane. Let $$\mathcal {T}_D$$ be set all plane spanning trees on and {F}(\mathcal {T}_D)$$ compatibility that has vertex for each element in vertices adjacent only corresponding compatible. We show, one hand, connected cylindrical, monotone, or strongly c-monotone drawing. On other we...

Abstract Is it always beneficial to create a new relationship (have follower/friend) in social network? This question can be formally stated as property of the centrality measure that defines importance actors network. Score monotonicity means adding an arc increases score target arc; rank improves relatively remaining nodes. It is known most centralities are both and monotone on directed, stro...

Let [Formula: see text], [Formula: see text], and [Formula: see text] be a strongly monotone and Lipschitz mapping. A Krasnoselskii-type sequence is constructed and proved to converge strongly to the unique solution of [Formula: see text]. Furthermore, our technique of proo f is of independent interest.

We discuss the relation between (topological) transitivity and strong transitivity of dynamical systems. We show that a transitive and open self-map of a compact metric space satisfying a certain expanding condition is strongly transitive. We also prove a couple of results for interval maps; for example it is shown that a transitive piecewise monotone interval map is strongly transitive.

We consider a second order dynamical system for solving variational inequalities in Hilbert spaces. Under standard conditions, we prove the existence and uniqueness of strong global solution proposed system. The exponential convergence trajectories is established under pseudo-monotonicity Lipschitz continuity assumptions. A discrete version leads to relaxed inertial projection algorithm whose l...