Fractal Interpolation over Nonlinear Partitions

TL;DR

This paper extends fractal interpolation to domains with nonlinear partitions, offering a new comprehensive approach and conditions for unique solutions in certain function spaces.

Contribution

It introduces a generalized fractal interpolation framework over nonlinear partitions, expanding existing methodologies and providing conditions for solution uniqueness.

Findings

Established sufficient conditions for unique solutions.

Generalized fractal interpolation to nonlinear partitions.

Provided a holistic approach to fractal functions.

Abstract

This paper introduces the fractal interpolation problem defined over domains with a nonlinear partition. This setting generalizes known methodologies regarding fractal functions and provides a new holistic approach to fractal interpolation. In this context, perturbations of nonlinear partition functions are considered and sufficient conditions for the existence of a unique solution of the underlying fractal interpolation problem for some classes of function spaces are given.