Fractal Interpolation over Curves

TL;DR

This paper extends fractal interpolation methods to curves in Banach spaces, generalizing existing techniques and opening new avenues for interpolation over Banach submanifolds.

Contribution

It introduces a novel approach for fractal interpolation over curves in Banach spaces, significantly broadening the scope of existing methods.

Findings

Extended fractal interpolation to Banach space curves

Generalized methods to Banach submanifolds

Paved way for future research in fractal interpolation

Abstract

This paper introduces the novel concept of fractal interpolation over curves in Banach spaces. The contents are based on the usual methodologies involving the fractal interpolation problem over intervals but the current approach considerably extends and generalizes them and paves the way to fractal interpolation over Banach submanifolds.