AN ITERATIVE METHOD FOR A NONLINEAR EQUATION GOVERNED BY ACCRETIVE NONEXPANSIVE MAPPINGS IN BANACH SPACES

The nonlinear equation x + Tx = y is studied, where T is an m-accretive, nonexpansive mapping on a q-uniformly smooth Banach space with q is an element of (1, 2]. A Mann iterative process is proved to strongly converge to the unique solution of the equation. An estimates of convergence rate of the process is also given. The results of the paper extend those of Dotson [10] from the Hilbert space setting to a Banach space setting.

Automated summary

This paper investigates the nonlinear equation x + Tx = y, where T is an m-accretive, nonexpansive mapping on a q-uniformly smooth Banach space with q in (1, 2]. It is proven that a Mann iterative process strongly converges to the unique solution of the equation, and an estimate of the convergence rate is provided. The results of the paper expand upon Dotson's findings from Hilbert space to a Banach space setting.