An approximation solvability method for nonlocal differential problems in Hilbert spaces

Control Problems for Semilinear Neutral Differential Equations in Hilbert Spaces

We construct some results on the regularity of solutions and the approximate controllability for neutral functional differential equations with unbounded principal operators in Hilbert spaces. In order to establish the controllability of the neutral equations, we first consider the existence and regularity of solutions of the neutral control system by using fractional power of operators and the...

A viscosity approximation method for nonself operators and equilibrium problems in Hilbert spaces

Viscosity approximate methods have recently received much attention due to the applications in convex optimization problems. In this paper, we study a viscosity iterative algorithm with computational errors. Strong convergence theorems of solutions are established in the framework of Hilbert spaces. The main results presented in this paper improve the corresponding results announced recently. c...

Solvability of Nonlocal Fractional Boundary Value Problems

An iterative method for amenable semigroup and infinite family of non expansive mappings in Hilbert spaces

begin{abstract} In this paper, we introduce an iterative method for amenable semigroup of non expansive mappings and infinite family of non expansive mappings in the frame work of Hilbert spaces. We prove the strong convergence of the proposed iterative algorithm to the unique solution of a variational inequality, which is the optimality condition for a minimization problem. The results present...

Viscosity Approximation Methods for Equilibrium Problems and Zeroes of an Accretive Operator in Hilbert Spaces

In this paper, we establish a composite iteration scheme by the viscosity approximation method for finding a common element of the set of zero points of an accretive operator and the set of solutions of an equilibrium problem in the framework of a Hilbert space. Mathematics Subject Classification: 39B12, 47H06, 47H10