Superfractal Approximation of Functions

Abstract

The methods of superfractal approximation of sets introduced in 2005–2011 by M. Barnsley, et al. are modified for the approximation of functions. Nonlinear operators are introduced in the space of bounded functions. The limit behavior of this operator sequence is investigated in a function space (in a sense of pointwise and uniform convergence). We consider a nonhyperbolic case in which not all plane maps specifying the operator in the function space are contractive and propose sufficient conditions for the convergence of approximations and estimates of the errors for this kind of approximation (similar to the collage theorem for fractal approximation).