Concerning the vector-valued fractal interpolation functions on the Sierpiński gasket

MA Navascués, S Verma, P Viswanathan - Mediterranean Journal of …, 2021 - Springer
Mediterranean Journal of Mathematics, 2021Springer
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 RR
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 …
Abstract
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 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.
Springer
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