Iterative solution of nonlinear equations involving \(m\)-accretive operators in Banach spaces
We study the iterative process of solution of the nonlinear operator equation \[ x+ Ax=f,\quad x\in D(A),\;f\in X, \] where \(A: D(A)\subset X\to X\) is an \(m\)-accretive operator, \(X\) is a uniformly smooth Banach space. For \(X= H\), a Hilbert space, the problem above has been studied by Chidume and Dotson. Chidume considered iterative techniques in \(L_p\) spaces (\(2\leq p<\infty\) or \(1<p<2\)). Our theorems complement and generalize the results of Chidume.
scientific article; zbMATH DE number 710329