Abstract
The objective of this paper is to study the box-counting dimension of graphs of fractal interpolation functions and harmonic functions on the Sierpiński gasket. Firstly, we give construction of a fractal interpolation function on the Sierpiński gasket and then with the help of fractal interpolation functions we show the existence of fractal functions in the space dom(E) consisting of all finite energy functionals on the Sierpiński gasket. Later, we provide bounds for the box-counting dimension of graphs of some functions belonging to the family of continuous functions which arise as fractal interpolation functions. Moreover, we also obtain bounds for the box-counting dimension of graphs of harmonic functions and piecewise harmonic functions. Also, we obtain upper and lower bounds for the box-counting dimension of graphs of functions that belong to dom(E).
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