Ranking theory delivers an account of iterated contraction; each ranking function induces a specific iterated contraction behavior. The paper gives a complete axiomatization of that behavior, i.e., a complete set of laws of iterated contraction. It does so by showing how to reconstruct a ranking function from its iterated contraction behavior uniquely up to multiplicative constant and thus how ...

In this paper, the well known iterated Galerkin method and iterated Galerkin-Kantorovich regularization method for approximating the solution of Fredholm integral equations of the second kind are generalized to Hammerstein equations with smooth and weakly singular kernels. The order of convergence of the Galerkin method and those of superconvergence of the iterated methods are analyzed. Numeric...

From any given Iterated Function System, a small set of balls that cover the fractal attractor can be simply determined. This gives a priori bounds on the region of space in which the attractor may be constructed.

This paper deals with analytic families of holomorphic iterated function systems. Using real analyticity of the pressure function (which we prove), we establish a classification theorem for analytic families of holomorphic iterated function systems which depend continuously on a parameter when the space of holomorphic iterated function systems is endowed with the λ-topology. This classification...

In 1969, Kannan [1] proved a new mapping which improved the Banach Contraction theorem. The purpose of this paper is to generalize the Kannan mapping and also to prove it, in space of fractals.

Iterated function systems have been most extensively studied when the functions are affine transformations of Euclidean space and, more recently, projective transformations on real projective space. This paper investigates iterated function systems consisting of Möbius transformations on the extended complex plane or, equivalently, on the Riemann sphere. The main result is a characterization, i...

‘‘Iterated’’ multiperiod-ahead time series forecasts are made using a one-period ahead model, iterated forward for the desired number of periods, whereas ‘‘direct’’ forecasts are made using a horizon-specific estimated model, where the dependent variable is the multiperiod ahead value being forecasted. Which approach is better is an empirical matter: in theory, iterated forecasts are more effic...

Importance of contraction for belief change notwithstanding, literature on iterated belief change has by and large centered around the issue of iterated belief revision, ignoring the problem of iterated belief contraction. In this paper we examine iterated belief contraction in a principled way, starting with Qualified Insertion, a proposal by Hans Rott. We show that a judicious combination of ...