Further analysis of Multivariate fractal functions

TL;DR

This paper characterizes a multivariate fractal operator linked to fractal interpolation functions, explores its properties, extends it to L^p spaces, and investigates approximation capabilities of multivariate fractal functions.

Contribution

It introduces a new multivariate fractal operator, analyzes its properties, extends it to L^p spaces, and studies approximation features of multivariate fractal functions.

Findings

Characterization of the multivariate fractal operator

Extension of the operator to L^p spaces for p ≥ 1

Approximation properties of multivariate fractal functions

Abstract

The aim of this paper is to characterize a fractal operator associated with multivariate fractal interpolation functions (FIFs) and study the several properties of this fractal operator. Further, with the help of this operator, we characterize a latest category of functions and study their approximation aspects. The basic characteristics of this multivariate fractal operator's are given in several ways in this note. The extension of this fractal operator to the $L^p$-spaces for $ p \ge 1$ are also examined. Multivariate continuous fractal functions approximation characteristics are also examined.