Abstract The objective of this paper is to study the box-counting dimension of graphs of fractal interpolation functions and harmonic functions on the Sierpinski gasket. Firstly, we give construction of a fractal interpolation function on the Sierpinski 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 Sierpinski 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 ) .

中文翻译：

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关于谢尔宾斯基垫片上调和函数图的计箱维数

摘要 本文的目的是研究Sierpinski垫片上的分形插值函数图和调和函数图的计箱维数。首先，我们在Sierpinski垫片上构造了一个分形插值函数，然后借助分形插值函数，我们证明了在由Sierpinski垫片上的所有有限能量泛函组成的空间dom（E）中存在分形函数。稍后，我们为属于连续函数族的一些函数的图的框计数维度提供了边界，这些函数作为分形插值函数出现。此外，我们还获得了调和函数图和分段调和函数图的盒子计数维数的界限。还，