Approximation of fixed points of asymptotically demicontractive mappings in arbitrary Banach spaces.
Donatus Ikechi Igbokwe · 2002
ABSTRACT. Let E be a real Banach Space and K a nonempty closed convex (not necessarily bounded) subset of E. Iterative methods for the approximation of fixed points of asymptotically demicontractive mappings T: K → K are constructed using the more general modified Mann and Ishikawa iteration methods with errors. Our results show that a recent result of Osilike [3] (which is itself a generalization of a theorem of Qihou [4]) can be extended from real q-uniformly smooth Banach spaces, 1 < q < ∞, to arbitrary real Banach spaces, and to the more general Modified Mann and Ishikawa iteration methods with errors. Furthermore, the boundedness assumption imposed on the subset K in ([3, 4]) are removed in our present more general result. Moreover, our iteration parameters are independent of any geometric properties of the underlying Banach space.