Feasibility Problem In Hilbert Spaces Research Articles

Weak Convergence Theorems for Families of Nonlinear Mappings with Generalized Parameters

In this article, we first introduce new families of nonlinear mappings in a Hilbert space. Next, we consider iterative processes for the families with generalized parameters and then prove weak convergence theorems for finding common fixed points of the families. As applications, we obtain weak convergence theorems for finding solutions of variational inclusion problems, equilibrium problems, and split feasibility problems in Hilbert spaces. Our results generalize and improve related results in the literatures.

Iterative Methods for Generalized Split Feasibility Problems in Hilbert Spaces

Generalized split feasibility problems governed by generalized hybrid mappings are studied via iterative methods. Several algorithms are introduced to solve them. In particular, weak convergence of these algorithms is proved. As tools, averaged mappings and resolvents of maximal monotone operators are technically maneuvered to facilitate the argument of the proofs to the main results. Applications to Mann’s iteration method for nonexpansive mappings and to equilibrium problems are included.

A strong convergence theorem for equilibrium problems and split feasibility problems in Hilbert spaces

Abstract The main purpose of this paper is to introduce an iterative algorithm for equilibrium problems and split feasibility problems in Hilbert spaces. Under suitable conditions we prove that the sequence converges strongly to a common element of the set of solutions of equilibrium problems and the set of solutions of split feasibility problems. Our result extends and improves the corresponding results of some others. MSC:90C25, 90C30, 47J25, 47H09.

Weak convergence theorems of the modified relaxed projection algorithms for the split feasibility problem in Hilbert spaces

In this paper, we introduce a modified relaxed projection algorithm and a modified variable-step relaxed projection algorithm for the split feasibility problem in infinite-dimensional Hilbert spaces. The weak convergence theorems under suitable conditions are proved. Finally, some numerical results are presented, which show the advantage of the proposed algorithms.

General Split Feasibility Problems in Hilbert Spaces

Introducing a general split feasibility problem in the setting of infinite-dimensional Hilbert spaces, we prove that the sequence generated by the purposed new algorithm converges strongly to a solution of the general split feasibility problem. Our results extend and improve some recent known results.

Cyclic algorithms for split feasibility problems in Hilbert spaces

The split common fixed point problem (SCFPP) is equivalently converted to a common fixed point problem of a finite family of class- T operators. This enables us to introduce new cyclic algorithms to solve the SCFPP and the multiple-set split feasibility problem.

A System of Generalized Mixed Equilibrium Problems and Fixed Point Problems for Pseudocontractive Mappings in Hilbert Spaces

AbstractWe introduce and analyze a new iterative algorithm for finding a common element of the set of fixed points of strict pseudocontractions, the set of common solutions of a system of generalized mixed equilibrium problems, and the set of common solutions of the variational inequalities with inverse-strongly monotone mappings in Hilbert spaces. Furthermore, we prove new strong convergence theorems for a new iterative algorithm under some mild conditions. Finally, we also apply our results for solving convex feasibility problems in Hilbert spaces. The results obtained in this paper improve and extend the corresponding results announced by Qin and Kang (2010) and the previously known results in this area.

Solving stochastic convex feasibility problems in hilbert spaces

In a stochastic convex feasibility problem connected with a complete probability space (Ω,A,μ) and a family of closed convex sets (Cω)ωεΩ in a real Hilbert space H, one wants to find a point that belongs to Cω for μ almost all ω ε Ω. We present a projection based method where the variable relaxation parameter is defined by a geometrical condition, leading to an iteration sequence that is always weakly convergent to a μ almost common point. We then give a general condition assuring norm convergence of this equation to that μ almost common point