Iteration Methods for Approximation of Solutions of Nonlinear Equations in Banach Spaces

Abstract

The objective in this manuscript is to study some iterative methods used to approximate solutions of nonlinear equations in Banach Spaces. In particular, we study a Halperntype iterative scheme in relation to nonexpansive and asymptotically nonexpansive mappings and prove convergence theorems in both of these cases. We also study a hybrid steepest descent iterative scheme in relation to the variational inequality problem, and using this process, we prove convergence theorems for the approximation of the solution of the variational inequality problem in certain Banach spaces, in particular for Lp spaces.