Iterative Solution of Nonlinear Equations Involving m-Accretive Operators in Banach Spaces

Iterative Approximations of Zeroes for Accretive Operators in Banach Spaces

In this paper, we introduce and study a new iterative algorithm for approximating zeroes of accretive operators in Banach spaces.

Nonlinear Accretive Operators in Banach Spaces by Felix E. Browder

for each * in X. For any Banach space X and any element * of Xt J(x) is a nonempty closed convex subset of the sphere of radius ||x|| about zero in X*. If X* is strictly convex, J is a singlevalued mapping of X into X* and is continuous from the strong topology of X to the weak* topology of X*. J is continuous in the strong topologies if and only if the norm in X is C on the complement of the o...

Strong convergence theorem for finite family of m-accretive operators in Banach spaces

The purpose of this paper is to propose a compositeiterative scheme for approximating a common solution for a finitefamily of m-accretive operators in a strictly convex Banach spacehaving a uniformly Gateaux differentiable norm. As a consequence,the strong convergence of the scheme for a common fixed point ofa finite family of pseudocontractive mappings is also obtained.

ON COMPACT PERTURBATIONS AND COMPACT RESOLVENTS OF NONLINEAR m-ACCRETIVE OPERATORS IN BANACH SPACES

Several mapping results are given involving compact perturbations and compact resolvents of accretive and m-accretive operators. A simple and straightforward proof is given to an important special case of a result of Morales who has recently improved and/or extended various results by the author and Hirano. Improved versions of results of Browder and Morales are shown to be possible by studying...

A three-step iterative scheme for solving nonlinear φ-strongly accretive operator equations in Banach spaces