Local iterations for fixed points of uniformly hemicontractive maps in arbitrary normed linear spaces (Q2739278)

Let \(E\) be a real normed linear space and let \(T: D(T)\subset E\to E\) be a locally Lipschitz and uniformly hemicontractive map with open domain \(D(T)\) and a fixed point \(x^*\in D(T)\). The strong convergence of an iteration process to the fixed point of \(T\) is proved. Some results dealing with the solution of the equation \(Ax= f\), where \(A: D(A)\subset E\to E\) is locally Lipschitz and uniformly quasi-accretive with an open domain \(D(A)\), are obtained.