Wildness of Iteration of Certain Residue-Class-Wise Affine Mappings

Graph Theoretical Criteria for the Wildness of Residue-class-wise Affine Permutations

A permutation of Z is called residue-class-wise affine if there is a positive integer m such that it is affine on residue classes (mod m). The smallest such integer is called the modulus of the respective permutation. A residue-class-wise affine permutation is called tame if the moduli of its powers are bounded, and wild otherwise. In this article, we describe two criteria for deciding whether ...

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

Algorithms for a class of infinite permutation groups

Motivated by the famous 3n + 1 conjecture, we call a mapping from Z to Z residue-class-wise affine if there is a positive integer m such that it is affine on residue classes (mod m). This article describes a collection of algorithms and methods for computation in permutation groups and monoids formed by residue-class-wise affine mappings.

An Example of Data Dependence Result for The Class of Almost Contraction Mappings

In the present paper, we show that $S^*$ iteration method can be used to approximate fixed point of almost contraction mappings. Furthermore, we prove that this iteration method is equivalent to CR iteration method  and it produces a slow convergence rate compared to the CR iteration method for the class of almost contraction mappings. We also present table and graphic to support this result. F...

Strong convergence results for fixed points of nearly weak uniformly L-Lipschitzian mappings of I-Dominated mappings

In this paper, we prove strong convergence results for a modified Mann iterative process for a new class of I- nearly weak uniformly L-Lipschitzian mappings in a real Banach space. The class of I-nearly weak uniformly L-Lipschitzian mappings is an interesting generalization of the class of nearly weak uniformly L-Lipschitzian mappings which inturn is a generalization of the class of nearly unif...