Chapter 14. Computation of zeros of nonlinear monotone mappings in certain Banach spaces

Abstract

Let $E$ be a uniformly convex real Banach space with uniformly Gâteaux differentiable norm and $E^*$ its dual space and let $A : E \rightarrow E^*$ be a bounded and uniformly monotone mapping such that $A^{-1}(0)\not= \varnothing$. In this paper, we introduce an new explicit iterative algorithm that converges strongly to the unique zeros of $A$. The results proved here are applied to the convex optimization problem.