Approximation of fixed points of nonexpansive mappings and quasinonexpansive mappings in a Hilbert space

In this paper, we give a simple proof and some generalizations of results in Falset, Llorens-Fuster, Marino, and Rugiano (2016).Comment: 8 page

Ergodic approximations via matrix regularization approach

AbstractIn this paper we use a matrix approach to approximate solutions of variational inequalities in Hilbert spaces. The methods studied combine new or well-known iterative methods (as the original Mann method) with regularized processes that involve regular matrices in the sense of Toeplitz. We obtain ergodic type results and convergence

Viscosity Approximations by the Shrinking Projection Method of Quasi-Nonexpansive Mappings for Generalized Equilibrium Problems

We introduce viscosity approximations by using the shrinking projection method established by Takahashi, Takeuchi, and Kubota, for finding a common element of the set of solutions of the generalized equilibrium problem and the set of fixed points of a quasi-nonexpansive mapping. Furthermore, we also consider the viscosity shrinking projection method for finding a common element of the set of solutions of the generalized equilibrium problem and the set of fixed points of the super hybrid mappings in Hilbert spaces

On the Convex Feasibility Problem

The convergence of the projection algorithm for solving the convex feasibility problem for a family of closed convex sets, is in connection with the regularity properties of the family. In the paper [18] are pointed out four cases of such a family depending of the two characteristics: the emptiness and boudedness of the intersection of the family. The case four (the interior of the intersection is empty and the intersection itself is bounded) is unsolved. In this paper we give a (partial) answer for the case four: in the case of two closed convex sets in R3 the regularity property holds.Comment: 14 pages, exposed on 5th International Conference "Actualities and Perspectives on Hardware and Software" - APHS2009, Timisoara, Romani