A note on segmenting Mann iterates

Uniform asymptotic regularity for Mann iterates

In [16] we obtained an effective quantitative analysis of a theorem due to Borwein, Reich and Shafrir on the asymptotic behavior of general KrasnoselskiMann iterations for nonexpansive self-mappings of convex sets C in arbitrary normed spaces. We used this result to obtain a new strong uniform version of Ishikawa’s theorem for bounded C. In this paper we give a qualitative improvement of our re...

Mann iterates of directionally nonexpansive mappings in hyperbolic spaces

In a previous paper, the first author derived an explicit quantitative version of a theorem due to Borwein, Reich and Shafrir on the asymptotic behaviour of Mann iterations of nonexpansive mappings of convex sets C in normed linear spaces. This quantitative version, which was obtained by a logical analysis of the ineffective proof given by Borwein, Reich and Shafrir, could be used to obtain str...

A Note on Implicit and Explicit Mann Iterative Processes for Asymptotically Φ-Strongly Pseudocontractive Mappings

On Linear Dependence of Iterates

A functional equation related to a problem of linear dependence of iterates is considered.

On iterates of Möbius transformations on fields

Let p be a quadratic polynomial over a splitting field K, and S be the set of zeros of p. We define an associative and commutative binary relation on G ≡ K∪{∞}−S so that every Möbius transformation with fixed point set S is of the form x “plus” c for some c. This permits an easy proof of Aitken acceleration as well as generalizations of known results concerning Newton’s method, the secant metho...