Expression of Generalized Newton Iteration Method via Generalized Local Fractional Taylor Series

TL;DR

This paper reviews a generalized Newton iteration method based on local fractional Taylor series, utilizing fractal derivatives to solve equations involving fractal functions, with potential fixed points in generalized metric spaces.

Contribution

It introduces a generalized Newton iteration method derived from local fractional Taylor series and explores fixed point existence on fractal spaces.

Findings

Operators on fractal spaces are induced from Cantor sets.

Existence of generalized fixed points is established in fractal metric spaces.

The method extends classical Newton iteration to fractal functions.

Abstract

Local fractional derivative and integrals are revealed as one of useful tools to deal with everywhere continuous but nowhere differentiable functions in fractal areas ranging from fundamental science to engineering. In this paper, a generalized Newton iteration method derived from the generalized local fractional Taylor series with the local fractional derivatives is reviewed. Operators on real line numbers on a fractal space are induced from Cantor set to fractional set. Existence for a generalized fixed point on generalized metric spaces may take place.