Asymptotically Affine and Asymptotically Conformal Circle Endomorphisms

Dual Dynamical Systems for Circle Endomorphisms

We show that every uniformly asymptotically affine circle endomorphism has a uniformly asymptotically conformal (UAC) extension to the complex plane. Then we use the UAC extension to construct the dual dynamical system, the dual annulus, and the dual circle expanding map.

A Mean Ergodic Theorem For Asymptotically Quasi-Nonexpansive Affine Mappings in Banach Spaces Satisfying Opial's Condition

Convergence of an Implicit Iteration for Affine Mappings in Normed and Banach Spaces

Circle Endomorphisms, Dual Circles and Thompson’s Group

We construct the dual Cantor set for a degree two expanding map f acting as cover of the circle T onto itself. Then we use the criterion for a continuous function on this Cantor set to be the scaling function of a uniformly asymptotically affine UAA expanding map to show that the scaling function for f descends to a continuous function on a dual circle T∗. We use this representation to view the...

Stability and convergence theorems of pointwise asymptotically nonexpansive random operator in Banach space

In this paper, we prove the existence of a random fixed point of by using pointwise asymptotically nonexpansive random operator and the stability resultsof two iterative schemes for random operator.