This paper introduces a T−Da mapping that is weaker than the nonexpansive mapping. It introduces several iterations for the fixed point of the T−Da mapping. It gives fixed point theorems and convergence theorems for the T−Da mapping in Banach space, instead of uniformly convex Banach space. This paper gives some basic properties on the T−Da mapping and gives the example to show the existence of T−Da mapping. The results of this paper are obtained in general Banach spaces. It considers some sufficient conditions for convergence of fixed points of mappings in general Banach spaces under higher iterations.
Part of the book: Functional Calculus