Iterative Construction of Solutions to Nonlinear Equations of Strongly Accretive Operators in Banach Spaces

Abstract:

      In this paper, we investigate the Ishikawa iteration process in a p -uniformly smooth Banach space X . Motivated by Deng and Tan and Xu , we prove that the Ishikawa iteration process converges strongly to the unique solution of the equation Tx=f when T is a Lipschitzian and strongly accretive operator from X to X , or to the unique fixed point of T when T is a Lipschitzian and strictly pseudo contractive mapping from a bounded closed convex subset C of X into itself . Our results improve and extend Theorem 4. 1 and 4. 2 of Tan and Xu by removing the restrion in their theorems. These also extend Theorems 1 and 2 of Deng to the p - uniformly smooth Banach space setting.