Fixed points of several classes of nonlinear mappings in Banach space

In the first part of the paper conditions for the existence of ordinary and higher order fixed points of individual and commutative families of nonlinear operators are obtained.

The second part deals with the existence of fixed points of an operator $T:C \to X$ whose graph is closed in the Cartesian product topology induced by the strong topology in $C$ and the weak topology in $X$.

The convergence to fixed points of sequences of successive approximations is considered in both parts.