Concerning the Vector-Valued Fractal Interpolation Functions on the Sierpiński Gasket

The present paper is concerned with the study of vector-valued interpolation functions on the Sierpiński gasket by certain classes of fractal functions. This extends the known results on the real-valued and vector-valued fractal interpolation functions on a compact interval in R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {R}}$$\end{document} and the real-valued fractal interpolation on the Sierpiński gasket. We study the smoothness property of the vector-valued fractal interpolants on the Sierpiński gasket. A few elementary properties of the fractal approximants and the fractal operator that emerge in connection with the vector-valued fractal interpolation on the Sierpiński gasket are indicated. Some constrained approximation aspects of the vector-valued fractal interpolation function on the Sierpiński gasket are pointed out.