Mahdi Mirzapour - Assistant Professor, Department of Mathematics, Bu-Ali Sina University, Hamedan, Iran

In this paper, we study a fixed point iteration method based on generalized relaxation of string averaging operator. The string averaging operator will be constructed such a way that each string be made by composition of finitely many strictly quasi-nonexpansive operators. The constructed iterative method includes wide class of iterative methods for solving linear systems of equations (inequalities) and fixed-point iterations for solving nonlinear convex feasibility problems. To illustrate the performance of using generalized relaxation, some experiments in image reconstruction from projections is presented.

Convex feasibility problem, Generalized relaxation, Quasi-nonexpansive operators, String averaging