Approximation of Fixed Points of Lipschitz Pseudo-contractive Mappings

In Chapter 10, we stated the Ishikawa iteration theorem (Theorem 10.1) which converges strongly to a fixed point of a Lipschitz pseudo-contractive map T defined on a compact convex subset of a Hilbert space.

It is still an open question whether or not Theorem 10.1 can be extended to Banach spaces more general than Hilbert spaces. However, two other iteration methods have been introduced and have successfully been employed to approximate fixed points of Lipschitz pseudo-contractive mappings in certain Banach spaces more general than Hilbert spaces.